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Early-Age Cracking of Concrete Bridge Deck Slabs Reinforced with
GFRP Bars
by
Amir Ghatefar
A Thesis submitted to the Faculty of Graduate Studies of the University of
Manitoba in partial fulfillment of the requirements of the degree of
DOCTOR OF PHILOSOPHY
Department of Civil Engineering
University of Manitoba
Winnipeg, Manitoba, Canada
Copyright © 2015 by Amir Ghatefar
Abstract
ii
ABSTRACT
Since concrete bridge deck slabs are much longer in the traffic direction, they experience
transverse early-age cracks due to volumetric instability and restraint. In the last decade, the
lower cost of the non-corrodible Glass Fiber Reinforced Polymer (GFRP) bars, as alternative to
steel reinforcement, has made them attractive to the bridge construction industry. However, low
modulus of GFRP bars may lead to wider cracks in GFRP-RC structures. This serviceability
issue can be aggravated by harsh environmental conditions. Hence, the main objective of this
thesis is to investigate the effect of early-age cracking in restraint bridge deck slabs reinforced
with GFRP bars subjected to different environments. This research consists of two phases: an
experimental investigation and a numerical study. In the experimental phase, four full-scale cast-
in-place slabs reinforced with different longitudinal GFRP reinforcement ratios (0.30, 0.50, 0.70
and 1.1%) and one with steel reinforcement ratio of 0.7% measuring 2500 mm long × 765 mm
wide × 180 mm thick were constructed and tested in the laboratory. Three environmental
conditions were implemented; normal (laboratory) adiabatic conditions as well as freezing-
thawing and wetting-drying cycles. The main test results are presented in terms of cracking
pattern, width and spacing, and strains in the reinforcement and concrete. Test results indicated
that the minimum reinforcement ratio (0.7%) recommended by CHBDC for bridge deck slabs
reinforced with GFRP bars satisfied the serviceability requirements after being subjected to the
simulated exposures of normal laboratory conditions, freezing-thawing, and wetting-drying
cycles. In the numerical phase of this research, a finite element model (FEM) was constructed
using ATENA software package (ver. 5) to simulate the behaviour of the test specimens.
According to the FEM results, a reinforcement ratio of 0.45% Carbon FRP (CFRP) can control
the early-age crack width and reinforcement strain in CFRP-RC members subjected to restrained
Abstract
iii
shrinkage. Also, the results indicated that changing the bar surface texture (sand-coated and
ribbed bars) or concrete cover had an insignificant effect on the early-age crack behavior of FRP-
RC bridge deck slabs subjected to shrinkage. However, reducing bar spacing and concrete
strength resulted in a decrease in crack width and reinforcement strain.
Acknowledgment
iv
ACKNOWLEDGMENT
In the name of GOD
I would like to express my deepest gratitude to my supervisor, Dr. Ehab El-Salakawy, P.Eng.,
Professor of Civil Engineering and Canada Research Chair in Durability and modernization of
Civil Structures in the Department of Civil Engineering at the University of Manitoba. I greatly
appreciated his open door policy whenever problems, of which there were many, arose. He was
the one who initiated the idea of this research and he has been always my first resource for
creative ideas and helpful advices. Also, I would like to expresses my gratitude to my co-advisor
Dr. Mohamed Bassuoni, P.Eng., Associate Professor in the Department of Civil Engineering at
the University of Manitoba, for his encouragement and insightful and thoughtful feedbacks. His
deep, broad knowledge and experience have been of great value to me. This thesis would not
have been possible without his support.
In addition, the author would like to thank his colleagues for their support during all work stages.
Also, the assistance of the McQuade Heavy Structures Laboratory manager, Mr. Chad Klowak,
P.Eng and the technicians, Mr. Brendan Pachal and Mr. Grant Whiteside for providing valuable
technical support for the construction and testing of the specimens is greatly acknowledged.
The financial support provided by the Natural Science and Engineering Research Council of
Canada (NSERC) through Canada Research Chairs (CRC) program and the Network of Centers
of Excellence on Intelligent Sensing for Innovative Structures (ISIS Canada) are gratefully
appreciated.
Finally, I would like to acknowledge the undeniable role that my family had in all my life and
also in the past four years in the completion of my graduate studies. Mom and Dad, you were
always very supportive for the decisions that I have made in my life. Special thanks to my wife
Acknowledgment
v
“Mehrnaz” for her endless and enduring love and support. Raheleh, you are the best sister
anyone can have. I love you all and I am always grateful for having such a wonderful family.
Amir Ghatefar
Notations
vi
NOTATIONS
Ac: Agross - Afrp
Agross: overall gross section area of member (mm2)
AF: effect of air flow on concrete shrinkage (με)
AGFRP: total GFRP section area (mm2)
As: steel bar section area (mm2)
CFRP: carbon fiber reinforced polymer
𝐶1 : 2𝑠0
3𝐿 − 2𝑠0
𝐶𝑡ℎ: coefficient of thermal expansion (10-6
/°C)
db: re-bar diameter (mm)
d: effective depth (mm)
dt: temperature difference with respect to interior temperature (°C)
Ec (day): concrete modulus of elasticity at different age (days)
Ec (day): concrete modulus of elasticity at different age (days)
E*
e: effective concrete modulus of elasticity, 𝐸𝑒∗ :
𝐸𝑐(3)
1+𝜙∗
EGFRP: GFRP bar modulus of elasticity (GPa)
Es: steel modulus of elasticity (GPa)
f’c (day): concrete compressive strength at different age (days)
𝑓’𝑐𝑜: starting point of the non-linear curve (MPa)
Notations
vii
𝑓′𝑐𝑢: concrete cube strength (MPa)
fcm28(ACI 318-11a): concrete mean compressive strength(MPa)
f't (day): concrete tensile strength at different age (days)
ft (GFRP): tensile strength of GFRP bars (MPa)
𝑓𝑦: steel yield strength (MPa)
EF: FRP modulus of elasticity (GPa)
GFRP: glass fiber reinforced polymer
Gf: concrete fracture energy (MN/m)
h: ambient relative humidity (%)
h: overall height of member (mm)
K(h): ambient relative humidity factor for Bazant model (%)
KR: internal restraint factor
l: length parameter (m or mm)
Lc: element length scale parameter
m: number of cracks
Ncr: restraining force immediately after first cracking, 𝑁𝑐𝑟 : 𝑛 𝜌𝑓𝑡𝐴𝑐
𝐶1+𝑛𝜌(1+𝐶1)
N (∞): final tensile force (KN)
𝑛: 𝐸𝑠𝐸𝑐(3)
Notations
viii
𝑛∗ : 𝐸𝑠𝐸𝑒∗
RC: reinforced concrete
S: average crack spacing (m), 𝑆: 𝐿
𝑚
𝑠0 : 1.33𝑑𝑏10𝜌
t: slab thickness (mm)
t(day): time (day)
tc: concrete curing time (day)
T: ambient temperature (ºC)
v: volume of the submerged GFRP bars (ml.)
v/s: member’s volume-to-surface ratio (mm)
w: final cracking width (mm)
wd: end point of the softening curve (mm)
∆u: support displacement (mm)
β(h): ambient relative humidity factor for GL200 model (%)
βRH(h): ambient relative humidity factor for CEB-MC90 model (%)
βas(t): time development function of autogenous shrinkage
γsh: cumulative product of the applicable correction factors for fresh concrete properties and
ambient humidity conditions (using ACI 209.2R-08)
Notations
ix
ΔT: temperature change (ºC)
ε*sh: ultimate shrinkage strain (using ACI 209.2R-08)
εsh∞: notional ultimate shrinkage for Bazant model (mm/mm)
εshu: notional ultimate shrinkage for GL 2000 model (mm/mm)
εcso: notional ultimate shrinkage for CEB-MC90 model (mm/mm)
εcdso( fcm28): nominal drying shrinkage coefficient (mm/mm)
εTotal: shrinkage strain of concrete subjected to different environmental conditions (mm/mm)
𝜀𝑐𝑝: value of plastic strain at the max compressive strength
ρfrp: reinforcement ratio, Afrp/Ac
σ: concrete compressive stress (MPa)
σav: estimate of the average concrete stress in the period after first cracking, 𝜎𝑎𝑣 : 𝜎𝑐1+𝑓𝑡(7)
2
σc1: concrete stress away from the crack immediately after first cracking, 𝜎𝑐1 : 𝑁𝑐𝑟 (1+𝐶1)
𝐴𝑐
σ*
c1: final concrete stress away from the crack, 𝜎𝑐1∗ :
𝑁(∞)−𝜎𝑠1∗ 𝐴𝑠
𝐴𝑐
σ*
s2: final bar stress at the crack, 𝜎𝑠2∗ :
𝑁(∞)
𝐴𝑠
σ*
s1: final bar stress away from the crack, 𝜎𝑠1∗ :
−2𝐴𝑠0𝑚
3𝐿−2𝑠0𝑚𝜎𝑠2∗ +
3∆𝑢𝐸𝑠
3𝐿−2𝑠0𝑚
ϕ*: creep coefficient (using ACI 209.2R-08)
Table of Contents
x
TABLE OF CONTENTS
ABSTRACT………………………………………………………………...…………………….ii
ACKNOWLEDGMENT................................................................................................................ iv
NOTATION………………………………………………………………...…………………….vi
LIST OF TABLES ....................................................................................................................... xvi
LIST OF FIGURES ................................................................................................................... xviii
CHAPTER 1: INTRODUCTION .................................................................................................. 1
1.1 GENERAL…………………………………………………………………………………….1
1.2 PROBLEM DEFINITION ........................................................................................................ 1
1.3 SCOPE OF RESEARCH .......................................................................................................... 3
1.4 RESEARCH OBJECTIVES ..................................................................................................... 4
1.5 METHODOLOGY AND APPROACH ................................................................................... 4
1.6 THESIS ORGANIZATION...................................................................................................... 5
CHAPTER 2: LITERATURE REVIEW ....................................................................................... 9
2.1 GENERAL…………………………………………………………………………………….9
2.2 FRP COMPOSITE MATERIALS ............................................................................................ 9
2.2.1 Constituent Materials ...................................................................................................... 9
2.2.2 Physical Properties ........................................................................................................ 11
2.2.3 Mechanical Properties................................................................................................... 12
2.2.5 Design of Concrete Structure Using FRP ..................................................................... 12
2.3 SHRINKAGE OF CONCRETE ............................................................................................. 12
2.3.1 Plastic Shrinkage........................................................................................................... 14
2.3.2 Drying Shrinkage .......................................................................................................... 15
2.3.3 Autogenous Shrinkage .................................................................................................. 15
2.3.4 Carbonation Shrinkage ................................................................................................. 15
2.3.5 Shrinkage Strain Prediction .......................................................................................... 15
2.4 THERMAL CONTRACTION OF CONCRETE ................................................................... 17
2.5 SHRINKAGE AND TEMPERATURE CRACKING OF RESTRAINED CONCRETE ...... 19
2.6 FACTORS RELATED TO DESIGN ..................................................................................... 21
2.6.1 Longitudinal Reinforcement ......................................................................................... 21
Table of Contents
xi
2.6.1.1 Code provisions ................................................................................................ 24
2.6.2 Concrete Cover ............................................................................................................. 24
2.6.3 Thickness of Concrete Deck Slab ................................................................................. 25
2.6.4 Stiffness of Bridge Girders ........................................................................................... 25
2.6.5 Type and Spacing of Girders and End Support Condition ........................................... 26
2.7 FACTORS RELATED TO CONCRETE MATERIALS ....................................................... 28
2.7.1 Cement Type ................................................................................................................. 28
2.7.2 Cement Content ............................................................................................................ 28
2.7.3 Water Content ............................................................................................................... 29
2.7.4 Water-to-Cement Ratio ................................................................................................. 29
2.7.6 Air Content ................................................................................................................... 30
2.7.7 Silica Fume ................................................................................................................... 31
2.7.7.1 Effect of silica fume on plastic shrinkage and drying shrinkage ..................... 31
2.7.7.2 Effect of silica fume on autogenous shrinkage ................................................ 31
2.7.8 Fly Ash .......................................................................................................................... 32
2.7.9 Fibre-Reinforced Concrete ........................................................................................... 33
2.7.10 Shrinkage Reducing Admixture.................................................................................. 33
2.7.11 Aggregate Size ............................................................................................................ 33
2.7.12 Concrete Properties ..................................................................................................... 34
2.7.13 Creep of Concrete ....................................................................................................... 34
2.7.14 Modulus of Elasticity of Concrete .............................................................................. 34
2.7.15 Concrete Strength ....................................................................................................... 35
2.7.16 Coefficient of Thermal Expansion .............................................................................. 36
2.8 FACTORS RELATED TO ENVIRONMENT ....................................................................... 36
2.8.1 Hot Weather .................................................................................................................. 37
2.8.2 Cold Weather ................................................................................................................ 38
2.8.3 Relative Humidity ......................................................................................................... 39
2.8.4 Effect of Wind .............................................................................................................. 39
2.8.5 Effect of Freeze-Thaw Conditions ................................................................................ 40
2.8.6 Effect of Wet-Dry Conditions....................................................................................... 41
2.9 FACTORS RELATED TO CONSTRUCTION PRACTICE ................................................. 41
Table of Contents
xii
2.9.1 Curing ........................................................................................................................... 41
2.9.2 Formwork...................................................................................................................... 42
2.10 CRACK WIDTH .................................................................................................................. 42
CHAPTER 3: EXPERIMENTAL PROGRAM .......................................................................... 45
3.1 GENERAL…………………………………………………………………………………...45
3.2 MATERIAL PROPERTIES ................................................................................................... 45
3.2.1 Concrete ........................................................................................................................ 45
3.2.2 Reinforcements ............................................................................................................. 45
3.3 EXPERIMENTAL PROGRAM ............................................................................................. 48
3.3.1 Characterization of the Concrete Mix ........................................................................... 48
3.3.2 Test Setup and Prototypes............................................................................................. 50
3.3.3 Test Parameters ............................................................................................................. 53
3.3.4 Instrumentations............................................................................................................ 54
3.3.5 Test Procedure .............................................................................................................. 57
3.3.6 Environmental Conditioning Schemes ......................................................................... 58
3.3.6.1 Freezing-thawing cycles ................................................................................... 58
3.3.6.2 Wetting-drying cycles ...................................................................................... 65
3.4 MICROSTRUCTURE TESTS ............................................................................................... 65
3.4.1 UPV Test....................................................................................................................... 67
3.4.2 Rapid Chloride Penetrability Test (RCPT) ................................................................... 68
3.4.3 Backscattered Scanning Electron Microscopy Test (BSEM) ....................................... 70
CHAPTER 4: RESULTS AND DISCUSSION - LABORATORY CONDITIONS .................. 72
4.1 GENERAL…………………………………………………………………………………...72
4.2 SLABS SUBJECTED TO LABORATORY CONDITIONS ................................................. 72
4.2.1 General Observation ..................................................................................................... 72
4.2.2 Characteristics of cracks ............................................................................................... 75
4.2.2.1 Slab SG1 ........................................................................................................... 75
4.2.2.2 Slab SG2 ........................................................................................................... 75
4.2.2.3 Slab SG3 ........................................................................................................... 75
4.2.2.4 Slab SG4 ........................................................................................................... 76
4.2.2.5 Slab SS ............................................................................................................. 76
Table of Contents
xiii
4.2.3 Tensile Strains in Reinforcement .................................................................................. 80
4.2.3.1 Slab SG1 ........................................................................................................... 80
4.2.3.2 Slab SG2 ........................................................................................................... 80
4.2.3.3 Slab SG3 ........................................................................................................... 80
4.2.3.4 Slab SG4 ........................................................................................................... 80
4.2.3.5 Slab SS ............................................................................................................. 81
4.2.4 Concrete Surface Strain ................................................................................................ 81
4.2.4.1 Slab SG1 ........................................................................................................... 81
4.2.4.2 Slab SG2 ........................................................................................................... 82
4.2.4.3 Slab SG3 ........................................................................................................... 82
4.2.4.4 Slab SG4 ........................................................................................................... 82
4.2.4.5 Slab SS ............................................................................................................. 83
4.3 DISCUSSION OF SLABS UNDER NORMAL LABORATORY CONDITIONS .............. 88
4.3.1 Crack Characteristics .................................................................................................... 88
4.3.2 Strains in Concrete ........................................................................................................ 90
4.4 THEORETICAL VS. EXPERIMENTAL RESULTS ............................................................ 91
CHAPTER 5: RESULTS AND DISCUSSIO-EFFECT OF ENVIRONMENTAL
CONDITIONS .................................................................................................. 96
5.1 GENERAL .......................................................................................................................... 96
5.2 GENERAL OBSERVATIONS .............................................................................................. 96
5.3 FREEZE-THAW EXPOSURE ............................................................................................... 97
5.4 WETTING AND DRYING EXPOSURE ............................................................................ 101
5.5 MATERIALS TESTS ........................................................................................................... 104
5.5.1 UPV Test (Ultrasonic Pulse Velocity Test) ................................................................ 105
5.5.2 RCPT Test (Rapid Chloride Permeability Test) ......................................................... 105
5.5.3 Microstructural Analysis............................................................................................. 108
CHAPTER 6: NUMERICAL ANALYSIS ............................................................................... 108
6.1 GENERAL………………………………………………………………………………….109
6.2 NUMERICAL STUDIES ..................................................................................................... 110
6.3 FINITE ELEMENT MODEL (FEM) ................................................................................... 110
6.3.1 Concrete ...................................................................................................................... 111
Table of Contents
xiv
6.3.2 Steel Support Plates .................................................................................................... 115
6.3.3 Reinforcing Bars ......................................................................................................... 115
6.3.4 Meshing of the Model ................................................................................................. 117
6.3.5 Shrinkage Profile ........................................................................................................ 117
6.3.6 Analysis ...................................................................................................................... 121
6.3.7 Model Verification ...................................................................................................... 122
6.3.7.1 Cracking pattern .................................................................................................... 123
6.3.7.2 Crack width ........................................................................................................... 123
6.3.7.3 Reinforcement strain ............................................................................................. 125
6.3.7.4 Model verification for slabs subjected to freeze-thaw and wet-dry cycles ........... 126
6.3.8 Parametric Study ......................................................................................................... 129
6.3.8.1 Concrete compressive strength ............................................................................. 130
6.3.8.2 Reinforcing bar spacing ........................................................................................ 131
6.3.8.3 Concrete cover ...................................................................................................... 131
6.3.8.4 Reinforcement type ............................................................................................... 131
CHAPTER 7: SUMMARY, CONCLUSIONS AND FUTURE WORK .................................. 138
7.1 SUMMARY………………………………………………………………………………...138
7.2 CONCLUSIONS................................................................................................................... 138
7.2.1 Conclusions from the Experimental Testing of Series (I) Specimens ........................ 139
7.2.2 Conclusions from the Experimental Testing of Series (II) Specimens ....................... 139
7.2.3 Conclusions from the Numerical Modeling (ATENA and Gilbert’s model) ............. 140
7.3 ENGINEERING SIGNIFICANCE…………………………………………………………144
7.4 RECOMMENDATIONS FOR FUTURE WORK ............................................................... 144
REFERENCES………………………………………………………………………...….…...146
APPENDIX A: SHRINKAGE PREDICTION MODELS ………. .......................................... A-1
A-1 DIFFERENT SHRINKAGE PREDICTION MODELS ..................................................... A-2
A-1.1 ACI 209R-92 Model Solution: .................................................................................. A-3
A-1.2 Bažant-Baweja B3 Model Solution ........................................................................... A-4
A-1.3 GL2000 model solution ............................................................................................. A-4
A-1.4 CEB MC90-99 model solution: ................................................................................. A-5
APPENDIX B: CALCULATION OF FINAL CRACK WIDTH AND REINFORCEMENT
STRAIN ……………….. ............................................................................... B-1
Table of Contents
xv
B-1 GILBERTS PREDICTION MODEL .................................................................................. B-2
List of Tables
xvi
LIST OF TABLES
1Table 2.1: Typical coefficients of thermal expansion (Reproduced from ACI, 2006) ................. 14
2Table 2.2: Typical mechanical properties of FRP reinforcing (reproduced from ISIS Canada,
2007 and Pultrall Inc. 2014) ........................................................................................... 14
3Table 2.3: Heat of hydration kJ/kg (Cal/kg) of typical cement components (Newman and Choo
2003) ............................................................................................................................... 19
4Table 2.4: Code provisions for temperature & shrinkage FRP reinforcement ............................. 27
5Table 2.5: Limits of crack widths for steel-reinforced structures (ACI Committee 224 2001) ... 43
6Table 3.1: Proportions of concrete per cubic meter ...................................................................... 47
7Table 3.2: Mechanical properties of sand-coated GFRP and steel bars ....................................... 47
8Table 3.3: Details of the parameters varied in the tests ................................................................ 56
10Table 4.1: Input data for parameters used in equations 1 to 3 ...................................................... 92
11Table 5.1: DME and RCPT results ............................................................................................. 107
12Table 6.1: Mechanical properties of GFRP, CFRP and steel bars ............................................. 116
13Table 6.2: Environmental conditions applied to the slabs versus the time of exposure ............. 119
14Table 6.3: The predicted and experimental values of free shrinkage ......................................... 121
15Table 6.4: Test matrix for the FEM ............................................................................................ 132
18Table A-1: Parameter ranges of each model .............................................................................. A-2
19Table A-2: Input values for theoretical equations to predict shrinkage ..................................... A-3
20Table A-3: The calculated shrinkage value according to different model solutions .................. A-6
21Table A-4: The calculated shrinkage value according to different concrete compressive strength
(CEB MC90-99 model solution) .................................................................................. A-7
22Table B-1: Input data for parameters used in Gilbert’s model ................................................... B-2
List of Tables
xvii
23 24Table B-2: The intermediate calculations for the theoretical predictions of crack width and the
stress on the GFRP bars ................................................................................................ B-5
List of Figures
xviii
LIST OF FIGURES
1Fig. 2.1: Stress strain relationship for fibrous reinforcement and matrix (reproduced from ISIS
manual No.3 2007). ........................................................................................................ 10
2Fig. 2.2: Stress-strain curve for different reinforcing materials (reproduced from ISIS Manual
No.3 2007). ..................................................................................................................... 13
3Fig. 2.3: Restrained shrinkage cracking (reproduced from ACI Committee 224 2001). ............. 20
4Fig. 2.4: Continuously restrained full length bridge deck slab (reproduced from Frosch et al.
2003). .............................................................................................................................. 21
5Fig. 2.5: Swelling and plastic settlement cracks. .......................................................................... 22
6Fig. 2.6: Typical composite bridge decks. .................................................................................... 27
7Fig. 2.7: Early-age shrinkage for different water-cement ratios in a mortar with 45% aggregate
(reproduced from Pease et al. 2005). .............................................................................. 30
8Fig. 2.8: Delayed cracking tendency from creep relaxation (reproduced from Brown et al. 2007).
........................................................................................................................................ 35
9Fig. 2.9: The magnitude of shrinkage for Three Different Curing Environments (reproduced from
Holt and Leivo 2000). ..................................................................................................... 38
10Fig. 2.10: Shrinkage vs. Time for Different Relative Humidity (reproduced from ACI Committee
224 2001). ....................................................................................................................... 40
11Fig. 2.11: The effect of concrete and air temperatures, relative humidity, and wind velocity on
rate of evaporation of surface moisture from concrete (reproduce from CSA/A23.1-14
2009). .............................................................................................................................. 43
12Fig. 3.1: Casting test cylinders. .................................................................................................... 49
13Fig. 3.2: Coefficient of thermal expansion sample. ...................................................................... 49
List of Figures
xix
14Fig. 3.3: Schematic diagram for test matrix. ................................................................................ 51
15Fig. 3.4: Deck slab dimensions (all dimensions are in mm): (a) side view, (b) top view, and (c)
cross-sections A-A .......................................................................................................... 52
16Fig. 3.5: General view of the test setup and specimen under normal laboratory conditions (all
dimensions are in mm). ................................................................................................... 53
17Fig. 3.6: General view of the test setup and specimen into the environmental chamber (all
dimensions are in mm). ................................................................................................... 55
18Fig. 3.7: Mid-length details. ......................................................................................................... 56
19Fig. 3.8: Typical instrumentation of deck slabs (all dimensions are in mm). .............................. 59
20Fig. 3.9: Measurement instruments; DAQ Amplifier, PI gauges, and Microscope. .................... 59
21Fig. 3.10: Slab ends effectively held in position and restrained against translation..................... 60
22Fig. 3.11: Formwork is thinly coated with oil to prevent adhesion of the concrete. .................... 60
23Fig. 3.12: Smooth supports at the bottom surface of the slabs to eliminate flexural action. ........ 61
24Fig. 3.13: Temperature control during the first 24 hours. ............................................................ 61
25Fig. 3.14: Water was poured into the surface reservoir (for slabs G-FT and G-WD). ................. 62
26Fig. 3.15: Equipment used in concrete material testing. .............................................................. 63
27Fig. 3.16: A part of the freeze-thaw profile for specimen G-FT. ................................................. 64
28Fig. 3.17: Relative humidity readings for the slab G-FT subjected to the freeze-thaw. ............... 64
29Fig. 3.18: Relative humidity readings for the G-WD subjected to wet-dry exposure. ................. 65
30Fig. 3.19: Taking cores from the slab. .......................................................................................... 66
31Fig. 3.20: UPV test machine. ........................................................................................................ 67
32Fig. 3.21: Disks preparation for RCPT. ........................................................................................ 68
33Fig. 3.22: RCPT test equipment. .................................................................................................. 69
List of Figures
xx
34Fig. 3.23: Backscattered scanning electron microscopy (BSEM). ............................................... 70
35Fig. 3.24: Typical prepared sample for the backscattered scanning electron microscopy (BSEM)
test. .................................................................................................................................. 71
36Fig. 4.1: Final crack pattern in the specimens. ............................................................................ 74
37Fig. 4.2: Internal strain of concrete at cracking at cracking time. ................................................ 74
38Fig. 4.3: Total free shrinkage of the plain concrete slab F. .......................................................... 77
39Fig. 4.4: Development of crack width with time (slab SG1). ....................................................... 77
40Fig. 4.5: Development of crack width with time (slab SG2). ....................................................... 78
41Fig. 4.6: Development of crack width with time (slab SG3). ....................................................... 78
42Fig. 4.7: Development of crack width with time (slab SG4). ....................................................... 79
43Fig. 4.8: Development of crack width with time (slab SS). ......................................................... 79
44Fig. 4.9: Average reinforcement strain (Top and Bot.) at cracking (slab SG1). .......................... 83
45Fig. 4.10: Average reinforcement strain (Top and Bot.) at cracking (slab SG2). ........................ 84
46Fig. 4.11: Average reinforcement strain (Top and Bot.) at cracking (slab SG3). ........................ 84
47Fig. 4.12: Average reinforcement strain (Top and Bot.) at cracking (slab SG4). ........................ 85
48Fig. 4.13: Average reinforcement strain (Top and Bot.) at cracking (slab SS). ........................... 85
49Fig. 4.14: Surface strains of concrete in the vicinity of the first crack (SG1). ............................. 86
50Fig. 4.15: Surface strains of concrete in the vicinity of the first crack (SG2). ............................. 86
51Fig. 4.16: Surface strains of concrete in the vicinity of the first crack (slab SG3). ..................... 87
52Fig. 4.17: Surface strains of concrete in the vicinity of the first crack (slab SG4). ..................... 87
53Fig. 4.18: Surface strains of concrete in the vicinity of the first crack (slab SS). ........................ 88
54Fig. 4.19: The final crack width and average reinforcement strain (Top and Bot.) at cracking
location. .......................................................................................................................... 90
List of Figures
xxi
55Fig. 4.20: Experimental and theoretical results for the final crack width. ................................... 94
56Fig. 4.21: Final experimental and theoretical results for the final stresses in GFRP bars at
cracking. .......................................................................................................................... 95
57Fig. 5.1: Final crack pattern in slabs G-FT and G-WD. .............................................................. 98
58Fig. 5.2: Internal strain of concrete at cracking at cracking time. ................................................ 98
59Fig. 5.3: Schematic of approximations of pore geometry in concrete. ......................................... 99
60Fig. 5.4: Crack width development in the specimen under freeze-thaw conditions. .................. 100
61Fig. 5.5: Crack width development in the slab G-FT under freeze-thaw conditions during first
and last cycles. .............................................................................................................. 100
62Fig. 5.6: Development of the bar strains in the slab G-FT under freeze-thaw conditions. ........ 102
63Fig. 5.7: Development of the bar strains in the slab G-FT under freeze-thaw conditions during
first and last cycles. ....................................................................................................... 102
64Fig. 5.8: Concrete surface appearance in different environmental conditions: (a) wet-dry, (b)
normal, and (c) freeze-thaw, and (d) Surface scaling mechanism. ............................... 103
65Fig. 5.9: Surface scaling. ............................................................................................................ 103
66Fig. 5.10: Crack width development in the slab G-WD under wet-dry conditions. ................... 104
67Fig. 5.11: Development of the bar strains in the slab G-WD under wet-dry conditions. ........... 106
68Fig. 5.12: Surface strain of the concrete in the vicinity of the first crack. ................................. 106
69Fig. 5.13: Chloride penetration depth in cores extracted from: (a) slab G-FT close to the crack
area, (b) slab G-FT out of the crack area, (c) slab G-WD close to the crack area (d) slab
G-WD out of the crack area. ......................................................................................... 107
List of Figures
xxii
70Fig. 5.14: Typical SEM micrographs from: (a) specimen G-WD (slab under wetting and drying
conditions), and (b) specimen G-FT (slab under freezing and thawing conditions) at
vicinity of the main crack. ............................................................................................ 108
71Fig. 6.1: Model geometry: (a) side view (b) 3D view of the analytical model based on the
experimental test specimens, and (c) locations of the reinforcing bars (all dimensions
are in mm). .................................................................................................................... 111
72Fig. 6.2 Different finite element types used: (a) top view of the finite element mesh of the
analytical model (b) brick element, and (c) tetrahedron element. ................................ 112
73Fig. 6.3: Van Mier compressive stress-strain relationship of the concrete: (a) non-linear
ascending part (b) linear descending (softening) part, and (c) stress-crack opening
according to Hodjik law (reproduced from Cervenka et al. 2012). .............................. 115
74Fig. 6.4: Bond-slip relationship for different types of reinforcement in concrete at 3 days (f`c=15
MPa). ............................................................................................................................ 117
75Fig. 6.5: Experimental and predicted shrinkage values. ............................................................. 122
76Fig. 6.6: Concrete stresses in the Y direction (MPa) and cracking pattern. .............................. 124
77Fig. 6.7: Experimental and FEM results for the development of crack width with time for slabs
SG2, SG3, SG4 and SS. ................................................................................................ 125
78Fig. 6.8: Experimental and FEM results for the development of bar strains at crack location for
slabs SG1, SG2, SG3 and SS. ....................................................................................... 126
79Fig. 6.9: Crack width development in the slab G-FT under freeze-thaw conditions during first
cycle. ............................................................................................................................. 128
80Fig. 6.10: Development of the bar strains in the slab G-FT under freeze-thaw conditions during
first. ............................................................................................................................... 128
List of Figures
xxiii
81Fig. 6.11: Crack width development in the slab G-WD under wet-dry conditions. ................... 129
82Fig. 6.12: Development of the bar strains in the slab G-WD under wet-dry conditions. ........... 129
83Fig. 6.13: Results of FEM for slabs with different concrete strength, (a) typical concrete stresses
in the Y direction (MPa) and cracking pattern (f’c = 30 MPa), and (b) development of
crack width and average reinforcement strain at cracking with time. .......................... 135
84Fig. 6.14: Results of FEM for slabs with different bar spacing: (a) typical concrete stresses in the
Y direction (MPa) and cracking pattern (for spacing: 255 mm), and (b) development of
crack width and average reinforcement strain at cracking with time. .......................... 136
85Fig. 6.15: Results of FEM for slabs with different concrete cover: (a) typical concrete stresses in
the Y direction (MPa) and cracking pattern (for cover: 5 mm), and (b) development of
crack width and average reinforcement strain at cracking with time. .......................... 136
86Fig. 6.16: Results of FEM for slabs with different bar type: (a) typical concrete stresses in the Y
direction (MPa) and cracking pattern for GFRP, (b) typical concrete stresses in the Y
direction (MPa) and cracking pattern for CFRP (c) development of crack width with
time, and (d) development of the bar strains at crack location for the FEM. ............... 137
87Fig. 6.17: The crack width and average reinforcement strain (Top and Bot.) at cracking location
for the FE models reinforced with CFRP bars at 112 days. ......................................... 137
88Fig. A-1: The final calculated shrinkage for different concrete strength (CEB MC90-99 model
solution). ..................................................................................................................... A-10
Chapter1: Introduction
1
CHAPTER 1: INTRODUCTION
1.1 GENERAL
In field conditions, transportation structures such as bridge deck slabs and barrier walls will
likely be subjected to temperature and humidity changes due to daily or seasonal conditions.
Typically, while the concrete is still plastic during the first 24 hours after casting, thermal
changes from hydration processes and environmental conditions increase the cracking tendency
(Byard et al. 2010). After hardening, ambient temperature and humidity fluctuations affect the
volume instability of concrete. Therefore, at early ages, these structural elements may be
subjected to different combinations of shrinkage and swelling due to thermal cycles (e.g.
heating-cooling, or freezing-thawing) and internal relative humidity fluctuation (e.g. wetting-
drying). It is well-documented that the primary cause of early-age transverse cracking of bridge
deck slabs is restraint to volumetric instability of concrete (Hadidi and Sadeghvaziri 2005; Mehta
and Montherio 20014). There are many factors affecting this type of cracking such as materials
properties, construction techniques, design practices, and environmental conditions.
Early-age cracking of concrete bridge deck slabs is a common problem in bridge construction all
over the world. As bridge deck slabs are typically much longer in one direction than the other,
volumetric changes due to shrinkage are more pronounced in the longitudinal direction. The
girders, however, restrain the deck slabs against shrinkage which induces stresses that result in
transverse cracks. The cracks, usually penetrating the full slab depth, are typically spaced 1.0 to
3.0 m apart along the span, and are commonly observed above the transverse reinforcing bars.
Full-depth cracks are generally considered the most severe form of bridge deck slab cracking
because they are additionally wide, which allows moisture and aggressive chemicals (e.g. de-
Chapter1: Introduction
2
icing salts) to infiltrate into the concrete rapidly. As a result, transverse deck slab cracking can
cause accelerated deterioration of reinforcing bars and concrete itself (Krauss and Rogalla 1996).
Recently, the non-corrodible fibre reinforced polymer (FRP) bars have been used as
reinforcement for concrete members to mitigate the corrosion problem of conventional steel
reinforcement. Among different types of FRP materials, the low cost of glass fibre reinforced
polymer (GFRP) bars makes them more amenable for the construction industry. Compared to
steel, GFRP bars have a lower modulus of elasticity, therefore, concrete elements reinforced with
GFRP bars exhibit larger deformation which causes wider cracks. Unlike steel, GFRP materials
do not corrode by nature; however, they may be susceptible to other forms of deterioration due to
harsh environments such as de-icing chemicals, sulfates, UV and alkali (ISIS Canada 2006). This
serviceability issue can be aggravated by harsh environmental conditions. A maximum crack
width of 0.5 mm is recommended by the Canadian Highway Bridge Design Code-CHBDC,
CAN/CSA-S6-06 (CSA 2006) for FRP-RC bridge components subjected to aggressive
environments and 0.7 mm for other bridge members. Cracks are the easiest place for moisture
and aggressive chemicals to accelerate the deterioration of GFRP bars as well as to shorten the
service life of concrete structures. Design codes and previous studies proposed different models
to calculate the maximum allowable crack width. These studies were based on cracks that are
perpendicular to the main reinforcing bars as a result of flexural loading. Although reinforcement
cannot stop cracking, placing longitudinal reinforcement can control both crack spacing and
crack width in bridge deck slabs. Guidelines for designing bridge deck slabs typically specify a
minimum amount of reinforcement to control cracks due to shrinkage or temperature changes.
However, limited research has investigated the effect of longitudinal GFRP bars on the early-age
transverse cracking of bridge deck slabs (Myers et al. 2003).
Chapter1: Introduction
3
1.2 PROBLEM DEFINITION
Early-age cracking is one of the main problems facing concrete structures reinforced with GFRP
bars, especially those having high surface-to-volume ratio such as bridge deck slabs, parking
garage structures, concrete pavements, and industrial floors. These structures have high tendency
to wide cracking, resulting from the restraint conditions, exposure to different environmental
conditions and low modulus of elasticity of reinforcement.
Currently, there are several codes and guidelines providing recommendations for the design and
construction of concrete structures reinforced with FRP materials, especially in USA and
Canada. Most of these codes and guidelines are based on modifying corresponding formulas
originally developed for steel bars and take into account the difference in properties and
behaviour between FRP and steel material. For example, in the CHBDC (CAN/CSA-S6-06), the
empirical design method for FRP-reinforced concrete (RC) cast-in-place bridge deck slabs
provides 0.0035 for each layer as a minimum reinforcement ratio in the longitudinal direction.
Moreover, based on an experimental study, Koenigsfeld and Myers (2003) concluded that the
equation listed in ACI-440.1R-03 (ACI Committee 440 2003) [earlier version of ACI Committee
440 2006] for minimum FRP reinforcement ratio was overly conservative; however, they did not
recommend any new equation to calculate minimum FRP reinforcement ratio. Although
numerous studies have investigated the cracking and fracture behavior of RC elements, scarce
data on restrained shrinkage cracking in FRP-RC elements have been reported under different
environmental conditions. Consequently, further research is still needed in this area. The current
study presents a research program evaluating the effect of longitudinal (secondary) GFRP
reinforcement ratio and configuration on early-age cracking of bridge deck slabs subjected to
Chapter1: Introduction
4
different environmental conditions such as adiabatic laboratory conditions as well as freezing-
thawing and wetting-drying cycles.
1.3 SCOPE OF RESEARCH
This research is mainly investigating the contribution of the longitudinal reinforcement in
controlling early-age cracking in FRP-RC structures. The scope of this program is to study cast-
in-place bridge deck slabs reinforced with sand-coated GFRP bars. Normal strength concrete mix
with silica fume admixture is used to represent the ultimate practical shrinkage strain. Only
direct tension induced as a result of restraint and volumetric changes of concrete is considered;
while, actions in the form of flexural loading causing flexural cracks are not included in the
scope of this study.
1.4 RESEARCH OBJECTIVES
This research is among the early studies investigating the effect of longitudinal (secondary)
GFRP reinforcement ratio on the early-age cracking of bridge deck slabs. Although many
researchers have examined the flexural cracking of reinforced concrete structures, very few
researches on restrained shrinkage cracking in reinforced concrete elements have been
investigated. Even fewer to no research has addressed the shrinkage cracking in concrete
elements reinforced with FRP under different environments, particularly for bridge deck slabs;
therefore, further research in this area is urgently needed.
The main objective of this research is to develop a suitable design methodology for determining
the minimum FRP reinforcement in bridge deck slabs to resist early-age cracking (with normal
strength concrete) under different environmental conditions, such as wetting-drying and
freezing-thawing cycles.
Chapter1: Introduction
5
In this context, the following specific objectives are identified:
Better understanding of the early-age behaviour of the GFRP-RC bridge deck slabs with
experimental set-up simulating restrained field conditions.
Investigating the applicability of currently available prediction/design models, design
codes and construction practices.
Investigating the effects of different ambient conditions such as freezing-thawing and
wetting-drying cycles on early-age transverse cracking of GFRP-RC bridge deck slabs.
Determining the minimum GFRP and CFRP reinforcement ratio for longitudinal bars in
the top and bottom assembly.
Investigating the effect of FRP bar spacing, bar surface texture, concrete cover and
concrete strength on early-age transvers cracking of FRP-RC bridge deck slabs.
1.5 METHODOLOGY AND APPROACH
This research consists of two phases: an experimental investigation and an analytical study. The
full-scale experimental study is performed to understand the restrained shrinkage cracking
problem. A novel test set-up is introduced which allows for simulating the restrained shrinkage
at early ages of bridge deck slabs.
The experimental phase includes two series. Series (I) consists of six full-scale specimens, which
are constructed and tested in the laboratory to investigate the effect of reinforcement ratio under
laboratory environmental conditions on early-age cracking in FRP-RC bridge deck slabs. These
specimens have variable longitudinal reinforcement ratio (cross-sectional area of GFRP bars).
Series (II) includes two specimens subjected to freezing-thawing and wetting-drying cycles. The
objective of the second series was to investigate the effect of harsh environmental conditions on
Chapter1: Introduction
6
the development of early-age cracking. The two specimens in this series are reinforced with the
minimum-acceptable reinforcement ratio as obtained by first series. All specimens are properly
instrumented to monitor strains, humidity, temperature history, and crack development. In
addition, tests to obtain concrete properties such as tensile and compressive strength and
modulus of elasticity are conducted. Also, to evaluate the internal conditions of the cementations
matrix and the interconnectivity of the pore structure, in the concrete slabs subjected to different
environmental conditions, materials tests are performed. These tests include the rapid chloride
penetrability test (RCPT) and the dynamic modulus of elasticity (DME) from the ultrasonic pulse
velocity (UPV).
The analytical phase of the research program consists of two stages. In the first stage, the
computer software ATENA (ver. 5 2013) is utilized to construct a finite element model (FEM)
for simulating restrained shrinkage bridge deck slabs. The most important parameters to consider
in a computer simulation of RC bridge deck slabs subjected to restrained shrinkage are tensile
fracturing of concrete and the effects of internal reinforcement to control the crack width. The
constructed numerical models are verified against the results of the laboratory specimens. In the
second stage, the verified model is used to investigate five key parameters known to affect early-
age cracking; namely, reinforcement spacing, reinforcement type and bar surface texture,
concrete compressive strength and thickness of concrete cover (top and bottom).
1.6 THESIS ORGANIZATION
This thesis consists of seven chapters. A brief description of each chapter is presented in the
following paragraphs.
Chapter1: Introduction
7
- Chapter one presents a general view of transverse early-age cracking in bridge deck slabs
reinforced with GFRP bars and the problems associated with it. It identifies the need for
further research that is required to improve the understanding of the early-age behaviour
of the GFRP-RC bridge deck slabs with experimental test set-up simulating restrained
field conditions, and describes the main objectives and scope of the Ph.D. research.
- A review of the characterization of GFRP reinforcement in concrete structures and
parameters that influence the early-age volumetric instability and restraint degree in high
surface-to-volume ratio structures are presented in Chapter two.
- Chapter three describes the test set-up, instrumentation, materials used, specimen details,
and testing procedure. Also, the environmental schemes applied in this study scheme are
presented in this chapter.
- The experimental results of Series (I) slabs subjected to shrinkage under normal
laboratory conditions are presented in Chapter 4. The results are presented in terms of
cracking pattern, crack width, strains in concrete and reinforcement in the vicinity of the
main crack location.
- The test results of Series (II) specimens exposed to freezing-thawing and wetting-drying
cycles are presented in Chapter 5. The results are presented in a similar manner to those
of Chapter 4.
- All the necessary steps to construct the FEM including material types, boundary
conditions, and the elements used in modeling along with verification of the model
against the experimental data are explained in Chapter 6. Also, the effect of five key
factors (concrete compressive strength, concrete cover, reinforcement surface texture,
Chapter1: Introduction
8
spacing and type) on early-age cracking in FRP-RC bridge deck slabs subjected to
shrinkage are presented in this chapter.
- Lastly, Chapter 7 presents a summary of the main findings and conclusions of the
research study and recommendations for further research.
Chapter 2: Literature Review
9
CHAPTER 2: LITERATURE REVIEW
2.1 GENERAL
In order to fully understand the transverse early-age cracking in bridge deck slabs, an extensive
literature review was performed. The problem in concern is controlling shrinkage cracking width
in concrete bridge deck slabs reinforced with GFRP bars. It should be noted that the research in
this area, including steel-RC structures, is very limited due to the difficulty in simulating
restrained conditions required to investigate shrinkage cracking problem in full-size specimens.
Since there are many factors affecting early-age cracking, such as material properties,
construction techniques, and design practices, part of the problem may arise from the fact that
materials engineers consider it as a structural problem, and the structural engineers consider it as
a material issue. Even when it is treated, both aspects are not usually considered. Although in
this study we are focusing upon the structural aspect, material aspects will be also considered to
fully understand the problem.
2.2 FRP COMPOSITE MATERIALS
2.2.1 Constituent Materials
The FRP products are composed of reinforcing fibres embedded in a matrix (resin) with some
additives and fillers. The high strength fibres exhibit ideal elastic behaviour providing strength
responsible for carrying the load (Fig. 2.1). The cohesive resin keeps the fibres together and
provides lateral support for them against buckling. Also, the resin can protect the fibres from
environmental and mechanical damage.
Chapter 2: Literature Review
10
The mechanical properties of the FRP composite depend on different parameters such as fibres
volumetric ratio, quality, shape, and orientation and resin type. Also, the manufacturing quality
control is an important consideration to guarantee a high quality product.
1Fig. 2.1: Stress strain relationship for fibrous reinforcement and matrix (reproduced from ISIS
manual No.3 2007).
Aramid, carbon, and glass are the mostly used fibres for FRP reinforcement products (ACI
1996). The aromatic polyamide fibre (AFRP) offers the highest tensile strength-to-weight ratio,
impact resistance, and toughness in comparison with CFRP and GFRP fibres. Also they are
resistant to carbon-based solvents, lubricants, and fuels. Aramid fibres are mainly used in
aerospace and marine applications. The main disadvantages of AFRP products are their difficulty
in cutting or machining and also low compressive strengths. The carbon fibres’ precursors are
one of the three types of pitch, rayon or polyacrylonitrile (PAN) fibres. The high tensile
modulus-to-weight ratio as well as tensile strength-to-weight ratio, and high fatigue strengths are
the main advantageous of CFRP products. They are most commonly used in the aerospace
industry. Nevertheless, the disadvantages of these composites are their low impact resistance,
high cost and high electrical conductivity. Two forms of Glass fiber can be produced, continues
Chapter 2: Literature Review
11
and staple fiber. Both forms are made by the same production method up to the fiber-drawing
stage. Ingredients such as sand, limestone, and alumina are dry-mixed and melted in a refractory
furnace. The temperature of the melt varies for each fiber-drawing furnace in the direct melt
process, or flows into drawn into fibers. Most glass fibers are currently produced by the direct
melt process. The advantages of glass fibres are lower cost (compared to other types), high
tensile strength, excellent resistance to compact and very low conductivity for both thermal and
magnetic. However higher density, weak stiffness, lower resistance to fatigue, sensitively to
abrasion and corrosion to alkaline solutions, and absorption of moisture can be considered as
disadvantages of glass fiber reinforced polymer.
The selection of appropriate resin plays an important role in the final mechanical properties and
quality of the FRP composite. Thermosetting and thermoplastic are the two main types of
polymeric matrices (resin) used for FRP products. Thermoplastic polymer are connected together
by weak bonds that can be broken by pressure or heat, while thermosetting polymers form a solid
matrix that once set, cannot be reformed again by neither pressure nor heat.
The use of additives and fillers in the FRP composites can perform number of additional
advantages such as fire resistance, coloration, and viscosity control. Also they can improve the
performance of the FRP products that might not be achieved by the other FRP components.
2.2.2 Physical Properties
Generally, the physical properties of the composite material are attributed to their coefficients of
thermal expansion (CTE) and density features. Fibre reinforced polymers bars as heterogeneous
materials have different CTE values in the transverse and longitudinal directions. Basically the
coefficient of thermal expansion in the longitudinal direction is dominated by the fibre properties,
Chapter 2: Literature Review
12
while the transverse coefficient is governed by the resin properties (ACI 2006). Typical CTE
values for steel and different FRP composite bars are shown in Table 2.1.
2.2.3 Mechanical Properties
Figure 2.2 shows the typical linear-elastic performance of different FRP reinforcements along
with steel bars up to failure. It should be noted that, none of the FRPs show ductile behaviour
with typical yielding plateau as the steel bars do. However, they have higher tensile strength and
lower modulus of elasticity than that of the conventional steel.
The mechanical properties of FRP bars rely on the volumetric ratio and type of fibres in the
composite, type of resin, and manufacturing quality control. Table 2.2 shows the typical
mechanical properties of available FRP reinforcing bars.
2.2.5 Design of Concrete Structure Using FRP
The design philosophy of the concrete structures using FRP reinforcement is different from that
of conventional steel-reinforced concrete. This is referred to the following differences in their
mechanical behaviour. The FRP are characterized by high tensile strength only in the direction of
the longitudinal fibres (as anisotropic material). This anisotropic behaviour affects the dowel
action and shear strength of FRP bars. Moreover, FRP materials do not show ductile behaviour
with yielding plateau, they are elastic until failure, and consequently design procedures should
account for a sudden failure in FRP-RC structures.
2.3 SHRINKAGE OF CONCRETE
Shrinkage is observed in both hardened and fresh states of concrete. The loss of water from the
capillary or gel pores is the main cause of shrinkage from its fresh state to later in life. The loss
of water from the capillaries or gel-pores results in internal relative humidity gradients in the
Chapter 2: Literature Review
13
concrete. The empty capillaries attract water molecules from the surface of the calcium silicate
hydrates; therefore, attraction force develops between calcium silicate hydrate particles. This
attraction force causes the concrete mass to shrink (Newman and Choo 2003). According to the
time of the appearance of the shrinkage, it can be classified in three main types; plastic,
autogenous, and drying shrinkage that occurred approximately within 30 min. to 6 hours, 1-28
days, and 1 day to 1 year, respectively (Mehta and Monterio 2014). The risk of early-age
cracking of concrete will be increased when the amount of early-age shrinkage of concrete
exceeds 1000 μm/mm (0.001 in./in.) (Transportation Research Circular E-C107 2006).
2Fig. 2.2: Stress-strain curve for different reinforcing materials (reproduced from ISIS Manual
No.3 2007).
Chapter 2: Literature Review
14
1Table 2.1: Typical coefficients of thermal expansion (Reproduced from ACI, 2006)
Direction
Coefficient of Thermal Expansion (×10-6
/ºC)
CFRP Steel AFRP GFRP
Longitudinal -1 to 0 11.7 -6 to -2 6 to10
Transverse 22 to 23 11.7 60 to 80 21 to 23
2Table 2.2: Typical mechanical properties of FRP reinforcing (reproduced from ISIS Canada,
2007 and Pultrall Inc. 2014)
FRP Type Trade Name
Modulus of
Elasticity
(GPa)
Tensile Strength
(MPa)
Ultimate tensile
Strain
Glass Fibre
V-RODTM
(LM) 42 940 0.022
V-RODTM
(HM) 63 1200 0.019
AslanTM
41 690 0.017
V-RODTM
(LM) 30 600 0.02
Carbon Fibre
V-RODTM
121 1597 0.014
AslanTM
123 2069 0.018
LeadlineTM
148 2251 0.016
NEFMACTM
1000 1201 0.013
2.3.1 Plastic Shrinkage
The evaporation rate of fresh concrete surface water in excess of 1.0 kg/m2 per hour is
considered to be critical where surface dries and plastic shrinkage occurs. Fresh concrete surface
water (due to bleeding) can be described as the upward movement of grout along with downward
movement of the heavier suspended aggregates within fresh concrete (Mehta et al. 2014).
Chapter 2: Literature Review
15
2.3.2 Drying Shrinkage
Concrete drying shrinkage can be described by three mechanisms: disjoining pressure, surface
tension, and capillary stress. However capillary stress appears to be the major mechanism in the
relative humidity range from 45% to 85%. During drying shrinkage the water evaporates from
the capillary or gel pores in the hardened concrete, consequently the tensile stresses, confined to
the surface tension of the water, are moved to the capillary pores resulting in the concrete
contraction (Newman and Choo 2003).
2.3.3 Autogenous Shrinkage
The water is consumed during the hydration process of cement paste, which reduces the relative
humidity of the concrete resulting in the autogenous shrinkage. This reduction of relative
humidity results in increasing the surface tension in capillary water. Autogenous shrinkage
occurs even if the concrete specimen is completely sealed from outer environment (TRB 2006).
This is contrary to drying shrinkage that occurs due to moisture transfer between concrete and
environment.
2.3.4 Carbonation Shrinkage
Cement paste reacts with carbon dioxide (CO2) during the hardening process; this reaction
increases the temperature (exothermal reaction) and weight of the concrete (Issa 1999). This
phenomenon causes shrinkage in the concrete. Carbonation shrinkage occurs only at early-age of
fresh concrete and it is not as significant as the other shrinkage types at early age.
2.3.5 Shrinkage Strain Prediction
ACI-209.2R 2008 offers different models such as ACI 209R-92 (Eq. 2.1), Bažant-Baweja B3
(Eq. 2.2), GL2000 (Eq. 2.3), and CEB MC90-99 (Eq. 2.4) to predict time dependent shrinkage of
Chapter 2: Literature Review
16
concrete. These empirical based models are applicable for the concrete moist cured at least for
one day. The shrinkage predicted methods were calibrated for the concrete containing silica fume
and fly ash less than 30% and compressive strength within 20-80 MPa. According to the
provided experimental data bank by Muller et al. 1999 for shrinkage, the Bažant-Baweja B3,
GL2000, and CEB MC90-99 methods can predict closest shrinkage value, while the ACI 209R-
92 model underestimates the concrete shrinkage.
εsh(t)(ACI 209) = –780γshf(t)(ACI 209)×10–6
[Eq. 2.1]
εsh(t)(B3)= –εsh∞k(h)S(t)(B3) [Eq. 2.2]
εsh(t)(GL2000) = –εshuβ(h)β(t)(GL2000) [Eq. 2.3]
where: γsh is the correction factor, f(t)(ACI 209), S(t)(B3), and β(t)(GL2000) are the time functions for ACI
209, Bazant, and GL 2000 models, respectively. εsh∞ and εshu are the nominal ultimate shrinkage
for Bazant, and GL 2000 equations, respectively. K(h) and β(h) is environmental relative humidity
factors for Bazant and GL 2000 models, respectively.
Among these models, CEB MC90-99 has been modified to take into account the particular
characteristics of concrete strength (for high strength concrete). This approach consists of
autogenous and drying shrinkage components. The total shrinkage of concrete can be calculated
by Eq. 2.4.
εsh(t,tc) = εcaso(fcm28)βas(t) + εcdso(fcm28)βRH(h)βds(t) [Eq. 2.4]
where: εcaso( fcm28) is the nominal autogenous shrinkage coefficient, and βas(t) is the time function
for autogenous shrinkage, εcdso( fcm28) is the nominal drying shrinkage coefficient, βRH(h) is the
environmental relative humidity, and βds(t) is time function for drying shrinkage.
Chapter 2: Literature Review
17
2.4 THERMAL CONTRACTION OF CONCRETE
Temperature changing can be associated with heat from an external (weather), and/or internal
sources (heat of cement hydration). Internal heat is produced during the hydration reaction
between cement and water (cement hydration is an exothermic process). The temperature rises
during time and reaches the peak temperature after approximately 10 to 20 hours after casting.
The peak temperature, which is derived as shown in the Eq. 2.5, depends on several factors such
as the content cement type, the environmental conditions at casting time, the type of formwork,
and the geometry of the member (Newman and Choo 2003). After reaching peak temperature,
the concrete starts to cool and reduce the volume.
Heat generated from hydration of 1 kg cement is about (Table 2.3):
H = 0.108 867 + 0.541 502 + 0.166 260 + 0.091 419 = 446 kJ/kg [Eq. 2.5]
Assuming the specific heat of concrete (energy) required to raise temperature of a material of
unit mass by one degree for normal concrete: 1~1.5 kJ/kgC and for water: 1 Cal/kgC = 4.18
kJ/kgC is around 1.3 kJ/kg C, the concrete cured in an adiabatic condition and cement content
per cubic meter of concrete is 470 kg, density of the concrete 2400 kg/m3, and coefficient of
thermal expansion (for concrete: gravel 12, granite 9, limestone 6, and Cement paste: 11 ~ 20) is
10-6/C:
The temperature increased due to hydration heat is
C
CkgkJmkg
mkgkgkJT
60
/3.1/2400
/420/4463
3
[Eq. 2.6]
Chapter 2: Literature Review
18
In the real situation, no matter how big is the concrete pour, concrete is not in adiabatic
condition, so temperature rise due to cement hydration is always lower than the derived value
from the compound hydration heat assuming adiabatic condition. It would be a rough guess that
470 kg per cubic meter of concrete would raise the temperature inside large concrete pour by
around 60C. The strain due to thermal gradient in concrete can be determined by Eq. 2.7 given
in ACI 209.2R 2008.
𝜀 = (𝐶𝑡ℎ)(𝑑𝑡)(𝐾𝑅) [Eq. 2.7]
Where:
𝜀: Induced tensile strain (10-6
), Cth: coefficient of thermal expansion (10-6
/°C), dt:
temperature difference with respect to interior temperature (°C), and KR: internal restraint
factor.
Assuming the concrete coefficient of thermal expansion: Cth = 19 10-6
/°C, temperature
difference with respect to interior temperature (°C): dt = (60-20) °C, and internal restraint factor:
KR = 1
The induced concrete strain due to the hydration temperature gradient is:
𝜀 = 19 10−6 40 1 = 760 με [Eq. 2.8]
Chapter 2: Literature Review
19
3Table 2.3: Heat of hydration kJ/kg (Cal/kg) of typical cement components (Newman and Choo
2003)
Compound Typical content
(%)
Heat of hydration kJ/kg
(Cal/kg)
C3A 10.8 867 (207)
C3S 54.1 502 (120)
C2S 16.6 260 (62)
C3AF 9.1 419 (100)
Minor Compound -
2.5 SHRINKAGE AND TEMPERATURE CRACKING OF RESTRAINED CONCRETE
If the volumetric change (specifically contraction) of concrete is restrained, tensile stresses will
induce in the concrete. If the developed tensile stresses are higher than the concrete tensile
strength, the concrete will crack (Fig. 2.3). The restraint can be internal, from reinforcement and
aggregate, or external, from the sub-base or superstructure of a bridge (Frosch et al. 2003). If
strains are not uniform throughout a member, as though produced by a thermal gradient, the
member itself can serve as a restraint. The magnitude of induced tensile stresses depends on both
the degree of restraint (how much movement is restricted) and the amount of shrinkage.
Bridge deck slabs are typically much longer in one direction than the other, thus volumetric
changes due to shrinkage and temperature changes are more pronounced in longitudinal
direction. Composite bridge deck slabs are continuously restrained with the girders. Since the
girders restrain the concrete bridge deck slabs against its volumetric instability (change), stresses
are induced on the bridge deck slabs that result in transverse cracks (Fig. 2.4) (Hadidi and
Sadeghvaziri 2005). Volumetric changes of concrete and degree of restraint against these
changes are greatly influenced by several factors, which are mainly related to concrete materials,
Chapter 2: Literature Review
20
concrete properties, structural design, construction practices and environmental conditions.
These factors are discussed in the following sections.
3Fig. 2.3: Restrained shrinkage cracking (reproduced from ACI Committee 224 2001).
Chapter 2: Literature Review
21
4Fig. 2.4: Continuously restrained full length bridge deck slab (reproduced from Frosch et al.
2003).
2.6 FACTORS RELATED TO DESIGN
Influences of different design factors on transverse cracking of bridge deck slabs are mainly due
to the restraint of volumetric instability of concrete. The effects of different design factors are
described briefly in the following sections.
2.6.1 Longitudinal Reinforcement
Transverse cracking of concrete bridge deck slabs are commonly observed directly above the top
reinforcing bars (Krauss and Rogalla 1996; Ramey et al. 1997). The effect of reinforcement on
the cracking tendency of concrete is found in both phases (fresh and hardened) of concrete. The
settlement of solids in the fresh concrete is hindered due to the presence of reinforcement
consequently; tensile stresses are produced above the reinforcing bars which cause plastic
settlement cracks (Fig. 2.5). Reinforcing bar size and spacing as well as clear concrete cover
thickness affect the magnitude of differential settlement greatly. Larger plastic settlement cracks
Chapter 2: Literature Review
22
develop for larger bar size and smaller cover thickness (Weyers et al. 1982; Dakhil et al. 1975).
The volumetric contraction of hardened concrete due to shrinkage or thermal changes is
restrained by reinforcement and produces tensile stress in the concrete. Reinforcing bar size,
type, spacing, and alignment affect the cracking tendency of concrete bridge deck slabs. Larger
bar size, and aligned transverse top and bottom bars create weakened cross-section of concrete
deck slab which is more susceptible to cracking.
On the other hand, the reinforcement can limit the concrete crack widening when the shrinkage
or thermal changes create tensile forces large enough to exceed the tensile strength of concrete.
Though the tensile stress is developed due to the internal restraint of reinforcement, it is very
small or negligible compared to external restraint such as restraint from composite girders and
the continuity of concrete deck slabs in bridges. Reinforcement cannot stop cracking of a
composite bridge deck slab but it can control the crack width.
5Fig. 2.5: Swelling and plastic settlement cracks.
Crack width depends on the bond between steel and concrete, reinforcement and concrete
quantity, distribution and size of bars, and degree of restraint (Gilbert 1992). Finer crack widths
Chapter 2: Literature Review
23
with uniform spacing can improve the serviceability and durability of bridge deck slabs. For
durability issues, shrinkage and temperature reinforcement as a minimum reinforcement is
mandatory in the most codes. Shrinkage and temperature reinforcement according to different
codes are presented in Table 2.4.
The amount of shrinkage and temperature reinforcements are suggested in the codes to control
cracking, however, problems related to early-age cracking still exist. Moreover, many
researchers introduced recommendations related to shrinkage and temperature reinforcement to
limit cracking, which can be summarized as follows:
As longitudinal steel reinforcing bars control transverse cracking, at least size 10M (11.3
mm-diameter) bars should be placed at a maximum spacing of 150 mm (6 in.) (Krauss
and Rogalla 1996).
About 0.60% of gross concrete area (Ag) is required as minimum steel reinforcement (As)
percentage to control cracks to a more acceptable level (ACI Committee 224 2001).
For restrained shrinkage, about three times the amount of minimum steel reinforcement
specified in ACI 318 code (Section 7.12) is required to control cracks (MacGregor and
Wight 2005).
For a fully-restrained slab, the shrinkage and temperature reinforcement should be two
times of that required by ACI 318 code (Gilbert 1992).
The total amount of longitudinal steel reinforcement to prevent uncontrolled crack
growth from yielding of the reinforcement can be calculated according to the following
equation (Frosch et al. 2003):
𝐴𝑠 =6√𝑓′𝑐
𝑓𝑦𝐴𝑔 [Eq. 2.9]
Chapter 2: Literature Review
24
2.6.1.1 Code provisions
The minimum FRP reinforcement ratio for shrinkage and temperature recommended in ACI-
440.1R-06 guidelines (ACI Committee 440 2006) has no experimental basis. It is noted that the
ACI-440.1R-06 limited the upper range for the ratio of temperature and shrinkage reinforcement
to 0.0036 (Table 2.4). Based on an experimental study, Koenigsfeld and Myers (2003) concluded
that the equation listed in ACI-440.1R-03 (ACI Committee 440 2003) [same as in ACI
Committee 440 2006] for minimum FRP reinforcement ratio was overly conservative; however,
they did not recommend any new equation to calculate minimum FRP reinforcement ratio.
Koenigsfeld and Myers (2003) found three times larger crack widths for GFRP specimens (1830
mm × 591 mm × 127 mm) than specimens of similar steel reinforcement ratio when subjected to
restraint shrinkage. They also concluded that twice as much GFRP reinforcement as steel is
required to achieve similar crack control characteristics when subjected to flexural loading. Due
to lower stiffness of GFRP bars, lower internal tensile stresses in concrete will develop due to
internal restraint from reinforcement against concrete shrinkage or temperature variations, which
leads to larger crack spacing followed by wider crack widths (Chen and Choi 2002). Though the
larger crack width is not a problem for FRP bars, maximum crack width must be limited due to
aesthetic reasons, aggressiveness of the environment, and anticipated service life of the structure
(ISIS Canada 2007). A maximum crack width of 0.5 mm is recommended by CHBDC (CSA
2006) for FRP-reinforced concrete components subjected to aggressive environment and 0.7 mm
for other members.
2.6.2 Concrete Cover
Concrete cover is essential to protect the reinforcement from aggressive environments and to
provide sufficient bond between reinforcing bars and concrete. All design codes for RC
Chapter 2: Literature Review
25
structures suggest minimum concrete cover depending on the exposure conditions of the
structure. Literature review indicates that concrete cover has an inconsistent influence on crack
development in bridge deck slab. Increased cover thickness reduces the tendency of cracking
(Ramey et al. 1997); however, concrete deck slabs with more than a 75-mm (3 in.) thick cover
are more susceptible to cracking (Myers 1982). Gilbert (1992) concluded that under direct
tension (due to shrinkage or thermal changes) cracks are more parallel-sided, which is different
from flexural cracks hence the magnitude of the crack width is less dependent on the concrete
cover.
2.6.3 Thickness of Concrete Deck Slab
Literature review indicates that thinner deck slabs are more susceptible to cracking than thicker
ones (Myers 1982; Ramey et al. 1997; French et al. 1999; Hadidi and Saadeghvaziri 2005).
Different minimum deck slab thicknesses were proposed to reduce deck slab cracking. Krauss
and Rogalla (1996) suggested a minimum of 200 to 300 mm (8 to 9 in.) thick deck slab; French
et al. (1999) recommended deck slab thickness not less than 160 mm (6 ¼ in.); Myers (1982)
observed that deck slabs thicker than 250 mm (10 in.) are less susceptible to cracking. On the
other hand, the deck slab itself can serve as a restraint if uniform shrinkage or temperature
changes are not developed throughout the deck slab. As shrinkage and temperature changes are
more uniform in thinner deck slabs than thicker one; thicker deck slabs may experience increased
stresses (Krauss and Rogalla 1996).
2.6.4 Stiffness of Bridge Girders
Several researchers suggested that lower section stiffness decreases the tendency of deck slab
cracking as the restraint of volume change of the deck slab is the main reason for deck cracking
(Krauss and Rogalla 1996; French et al. 1999; Ducret et al. 1997). Using finite-element models,
Chapter 2: Literature Review
26
Hadidi and Saadeghvaziri (2005) studied numerically the effect of section stiffness through
changing the moment of inertia of the composite section and found that the potential for the deck
slab cracking increased with the increase of composite section moment of inertia.
2.6.5 Type and Spacing of Girders and End Support Condition
Deck slabs compositely supported on steel girders (Fig. 2.6) have more cracking than those
supported on concrete girders (Krauss and Rogalla 1996; Frosch et al. 2003). It may be due to
the different coefficient of thermal expansion and higher thermal conductivity of steel girders
compared to those of concrete girders. Cracking is more prevalent on spans with fixed-ended
girders when compared to spans with pinned girders (Krauss and Rogalla 1996; French et al.
1999). Increased fixity (for example, bridge decks integrally built with abutment) increases crack
density near the supported end (Darwin et al. 2004).
Composite bridge deck slabs are more economic in comparison with the isolated deck slabs
(deck slabs just resting on girders). In order to get the benefits of arch action, the girder must be
connected to the concrete slab to transfer of longitudinal shear forces at the girder top flange-
concrete slab interface. When steel girders are used, the adequate connection is provided by
installing shear studs to the top flange of the steel girder. Furthermore, composite bridge deck
slab enhances the flexural capacity of the bridge deck slabs by providing internal arching actions
between the girders. Transverse cracking in bridge deck slabs are mainly due to this type of high
amount of external restraint. So, transverse cracking would be decreased with the decreasing of
this external restraint (Krauss and Rogalla 1996; French et al. 1999; Saadeghvaziri and Hadidi
2005). As deeper girders with closer spacing (stiffer girders) make deck slabs more susceptible
to cracking, shallower girders with wider spacing are recommended to control deck slab cracking
(Krauss and Rogalla 1996; Saadeghvaziri and Hadidi 2005).
Chapter 2: Literature Review
27
4Table 2.4: Code provisions for temperature & shrinkage FRP reinforcement
Code
[Clause]
Rebar
Type
Area
and/or
Ratio
Formula Spacing
Comments from
codes
ACI 440.1R-06
[Chapter 10]
FRP 𝐴𝑓𝑟𝑝/𝑑
= 0.0018 × (414/𝑓𝑓𝑢) × (Es/Ef)
≤ 0.0036
≤ 3h
≤ 300 mm
No experimental
data are available
for the minimum
FRP reinforcement
ratio for shrinkage
and temperature.
CHBDC (CSA
2006) [16.8.8.1]
GFRP 𝐴𝑓𝑟𝑝/𝑑
≤ 0.0035
(based on empirical method
for the longitudinal bars in the
bottom assembly and the
transverse and longitudinal
bars in the top assembly)
≤ 300 mm
CSA/S806-12
[8.4.2.3]
FRP 𝐴𝑓𝑟𝑝
= (400/EF)Ag > 0.0025Ag mm2
(in each of the two orthogonal
direction)
≤ 3h
≤ 300 mm
Es: Steel modulus of elasticity (GPa), EF: FRP modulus of elasticity (GPa), Afrp: FRP bar area (mm2), d:
effective depth (mm), ffu: design tensile strength of FRP (MPa), h: overall height of member (mm), Ag:
overall gross section area of member (mm2).
6Fig. 2.6: Typical composite bridge decks.
Chapter 2: Literature Review
28
2.7 FACTORS RELATED TO CONCRETE MATERIALS
Concrete is composed of cement paste and aggregates where cement paste acts as matrix and
aggregates act as rigid inclusion. The amount of shrinkage and heat of hydration are fully
dependent on the material properties of concrete and the ratio of constituent materials used in
concrete mixture. The following section describes the effects of different concrete constituent
materials on bridge deck slabs cracking.
2.7.1 Cement Type
The use of Type II cement is recommended in lieu of Type I cement by several researchers to
reduce the cracking tendency of concrete deck slab (Krauss and Rogalla 1996; Xi et al. 2003;
Hadidi and Saadeghvaziri 2005; Ramey et al. 1997). Type II cement has low heat of hydration
and thus lower thermal gradient and shrinkage. To fulfill the requirement of high early strength
to speed up form removal and access to the deck, fineness and composition of cement have been
changed during the last 20 to 30 years. The cement has become progressively finer. Higher heat
of hydration and greater shrinkage are the result of finer cement (Chariton and Weiss 2002;
Darwin et al. 2004). Type K shrinkage-compensating cement (ASTM C-845 1996) is another
type of cement that has been used to reduce early age cracking tendency in the bridge deck slabs
(Krauss and Rogalla 1996).
2.7.2 Cement Content
The use of low amount of cement in concrete mix is recommended by many researchers as
higher cement content produce higher temperature during hydration, shrinkage, and early-age
modulus of elasticity, and low creep (Krauss and Rogalla 1996; Xi et al. 2003). All of these
properties of concrete produced from the use of high content of cement have the marked adverse
effect on cracking tendency of concrete bridge deck slabs. Maximum amount of cement content
Chapter 2: Literature Review
29
has been recommended in different studies. French et al. (1999) and Hadidi and Saadeghvaziri
(2005) recommended minimizing the cement content to 386-392 kg/m3, while Xi et al. (2003)
recommended limiting the cement content to a maximum of 279 kg/m3 or less if possible.
2.7.3 Water Content
As the increase of water content increases the cracking tendency of concrete, reduction of water
content is recommended in many studies (Issa 1999; Darwin et al. 2004; NCHRP 2004).
However, Krauss and Rogalla (1996) found no correlation between cracking and water content in
the concrete deck slabs.
2.7.4 Water-to-Cement Ratio
Water-cement ratio has a very strong influence on the shrinkage of concrete and cement paste. It
is certain that high water-cement ratio leads to high shrinkage. Several studies recommended
reduction in the water-cement ratio in the concrete mix to reduce the cracking tendency of
concrete (French et al. 1999; Ramey et al. 1997; Xi et al. 2003). Maximum water-cement ratio
has been recommended in different studies, which ranges from 0.40 to 0.45. Some studies also
encouraged using water reducer to maintain water-cement ratio at 0.40 or lower. On the other
hand, resistivity against early-age cracking is questioned for using low water-cement ratio as it
results in high autogenous and plastic shrinkage, and less creep. High amount of shrinkage was
observed before initial set for low water-to-cement ratio; and after little expansion between
initial set and final set, shrinkage was continued after final set even under sealed condition (Fig.
2.7).
Chapter 2: Literature Review
30
7Fig. 2.7: Early-age shrinkage for different water-cement ratios in a mortar with 45% aggregate
(reproduced from Pease et al. 2005).
2.7.6 Air Content
French et al. (1999) suggested air entrainment of minimum 5.5 to 6 percent to reduce cracking.
Air entrainment is usually used to protect cracking due to freeze-thaw cycles by encapsulating
tiny air bubbles in the hardened concrete. Water freezing in the capillary pores leads to 9%
increase in volume. The resultant expansive force causes disruption of the pores if there is no
room for the ice to expand into. With sufficient air bubbles within the capillary network, the ice
can expand without causing disruption of the capillaries and thus prevents cracking. Again, the
addition of air entrainment will produce a more workable concrete for the same water-cement
ratio and thus less water (low water-cement ratio) can be used to get the desired level of
workability. Decreasing the water-cement ratio of concrete is believed to reduce drying and
plastic shrinkage and cracking tendency of concrete (French et al. 1999; Ramey et al. 1997).
Chapter 2: Literature Review
31
2.7.7 Silica Fume
Silica fume (micro-silica) is a by-product of the production of silicon and ferrosilicon alloys in
electric arc furnaces. The size of silica fume particles is approximately 100 times finer than
normal Portland cement. During the hydration of cement, calcium hydroxide is produced. Micro-
silica reacts with calcium hydroxide and produces calcium silicate hydrate (pozzolanic reaction).
Calcium silicate hydrate fills pores and decreases the permeability of concrete. The spaces
between cement grains are filled up by finer silica fume particles and also the spaces between
cement paste and aggregates. The result benefits to increase the strength of the concrete. Higher
heat of hydration is produced in silica fume concrete which causes higher thermal stress.
2.7.7.1 Effect of silica fume on plastic shrinkage and drying shrinkage
The loss of surface water (due to evaporation) cannot be readily replaced as the total amount and
the rate of bleeding of the concrete are decreased due to the hindrance of fine silica fume
particle. The result increases the shrinkage both in plastic and hardened concrete (Mehta et al.
2014).
2.7.7.2 Effect of silica fume on autogenous shrinkage
As the water chemically combined with the cement during hydration and specific volume of
chemically bound water is lower than specific volume of free water, volume of hydrated cement
paste is lower than the volume of cement and water (Powers and Brownyard 1947). This
shortage of free water supply results in an overall shrinkage as the cement hydrates. In the
normal concrete (where silica fume is not present), hydrated cement gel absorb the surrounding
free water and expansion of gel structure reduce the effect of shrinkage. However, when silica
fume is used with lower cement ratio, surrounding free water of concrete cannot enter into the
very low permeable gel to swell (silica fume form finer cement gel which occupies lower
Chapter 2: Literature Review
32
specific volume) and thus autogenous shrinkage is increased. The early-age cracking tendency of
silica fume concretes is higher than conventional concrete (Krauss and Rogalla 1996; Darwin et
al. 2004; Bloom and Bentur 1995). Whiting et al. (2000) found that the addition of silica fume
has little effect on both early-age and long-term shrinkage cracking if the silica fume concrete is
cured properly for at least seven days under moist condition. However, Whiting et al. (2000)
concluded that, the concrete mixtures with silica fume produces higher shrinkage than those
mixtures not containing micro-silica. Some studies suggested limiting the use of the amount of
silica fume to achieve the optimum results.
2.7.8 Fly Ash
Fly ash, similar to micro-silica, is also a pozzolanic material. Micro-silica accelerates the rate of
early-age strength gain and increases early concrete temperature, while fly ash retards the rate of
early-age strength gain and reduces the early concrete temperature. Fly ash is found to reduce the
calcium hydroxide content at 12 hours by delaying the formation of calcium hydroxide and
pozzolanic reaction can begin after 3 days (Weng et al. 1997). It is also found that reactivity of
calcium hydroxide with micro-silica is decreased when silica fume is used combined with fly
ash. Class C fly ash had smaller drying and autogenous shrinkage than the general used cement
paste mixture (Tangtermsirikul and Sudsangiam 1995). Brown et al. (2007) found that the use of
high volume of fly ash (55% of the Portland cement was replaced with Class F fly ash) in
concrete mixture had the best resistance to drying shrinkage cracking in concrete bridge deck
slabs. However, Mokarem et al. (2003) showed that the mixture containing fly ash exhibits
greater drying shrinkage compared to general used Portland cement mixture. Also Li et al.
(1999) showed that the width of early-age crack increases with increasing fly ash, micro-silica,
and calcium nitrate inhibitor.
Chapter 2: Literature Review
33
2.7.9 Fibre-Reinforced Concrete
The application of small fibres (steel, glass, polyvinyl alcohol, cellulose and polypropylene) in
concrete can reduce the shrinkage and thermal crack width. The distributed small fibres in the
concrete change the large discrete cracks into finer cracks along with improving the post-peak
ductility and increasing the concrete tensile strength (Hadidi and saadeghvaziri 2005).
2.7.10 Shrinkage Reducing Admixture
The main function of shrinkage reducing admixtures (SRA) is to reduce the drying shrinkage by
reducing the surface tension of the water in the capillary pores. If the surface tension of the water
is reduced, there is less tension transferred to the capillary walls, and consequently less
shrinkage. Weiss et al. (1998) found that the use of SRA in concrete mixture will prevent or
delay of cracking. Up to 45% reduction in free shrinkage was found after adding 2% SRA in
concrete mixture.
2.7.11 Aggregate Size
Largest possible size of a high quality, low shrinkage aggregate is suggested in several studies to
minimize the shrinkage of concrete. Maximum possible aggregate content that is high aggregate
to binder ratio is also recommended. The shrinkage of aggregates is very low (almost negligible)
compared to binder, which implies that the use high aggregate to binder ratio will reduce the
total amount of shrinkage of concrete. Also larger aggregate size is recommended to minimize
concrete shrinkage. They produce a rigid framework with the help of cement paste,
consequently, movement of aggregate is reduced as the shrinkage of cement paste cannot pull the
surrounding large aggregates closer (TBR 2006). Only micro cracks will be developed in cement
paste surrounding the aggregates. The water demand of the aggregate has also a major influence
on the shrinkage of concrete. ACI Committee 224 (2001) suggested aggregates with low
Chapter 2: Literature Review
34
absorption and high modulus of elasticity will provide a low shrinkage concrete. Lopez et al.
(2008) showed high performance concrete with pre-wetted expanded slate light weight aggregate
produces lower shrinkage and total creep than air-dried expanded slate light weight aggregate.
Lopez also concluded that compressive strength (56-day and 1-year) of pre-wetted expanded
slate light weight aggregate was higher than that of air-dried expanded slate light weight
aggregate due to the improved hydration afforded by the pre-wetted lightweight aggregate.
2.7.12 Concrete Properties
The properties of concrete are the reflection of mix design of concrete. Different concrete
properties such as creep, modulus of elasticity, compressive strength, and thermal expansion of
concrete have pronounced effect on bridge deck slabs cracking. Summary of the effect of
different concrete properties are given below:
2.7.13 Creep of Concrete
Creep has beneficial effects in reducing the restrained drying shrinkage. Tensile stress is
developed in the concrete from restrained drying shrinkage and thermal contraction. Creep leads
the concrete to flow in small amounts and can serve to relax shrinkage tensile stresses and
thereby, reduces the risk of cracking as shown in Fig. 2.8 (Brown et al. 2007). Therefore, higher
creep means lowering the cracking tendency.
2.7.14 Modulus of Elasticity of Concrete
Restrained shrinkage and temperature changes induce tensile stress in concrete which are
proportional to the modulus of elasticity of concrete. This means higher stress will develop for
higher modulus of elasticity, and thus, cracking tendency of concrete will increase (Hadidi and
Saadeghvaziri 2005).
Chapter 2: Literature Review
35
8Fig. 2.8: Delayed cracking tendency from creep relaxation (reproduced from Brown et al. 2007).
2.7.15 Concrete Strength
The application of high strength concrete (HSC) has been increased during the past decades. In
general, HSC is accompanied by an increase in the cement content and a decrease in the water-
to-binder ratio, which results in an increment of hydration temperature and autogenous
shrinkage. Therefore, compared to normal strength concrete, RC structures with HSC are more
susceptible to early-age cracking. The HSC offers high sectional stiffness (Sooriyaarachchi 2005);
thus structures made of HSC experience high tensile stress, and consequently, high cracking potential
for the same amount of shrinkage (Hadidi and Saadeghvaziri 2005). However, due to the higher
tensile strength of HSC, it also provides higher resistance to shrinkage and thermal cracking.
Hence, it is a challenge to maintain a proper balance between concrete strength, shrinkage and
other long-term properties (e.g. creep). Several studies investigated the effect of high strength
concrete on early-age cracking in bridge deck slabs. Darwin et al. (2004) found that high
compressive strength of concrete increased crack density for monolithic bridge decks. Petrou et
al. (2001) concluded that more appropriate high performance concrete (HPC) mix design (for
Chapter 2: Literature Review
36
enhanced durability characteristics not high-strength) is needed to be used in bridge deck slabs.
Weiss et al. (1998) recommended the use of a shrinkage reducing admixture (SRA) in HSC to
reduce the early-age cracking tendency in the structures with high surface-to-volume ratios.
2.7.16 Coefficient of Thermal Expansion
As the stresses developed in the deck slabs from a temperature change are linearly depend on the
concrete coefficient of thermal expansion (CTE), consequently, transverse thermal cracking can
be reduced by using lower CTE of concrete (Krauss and Rogalla 1996). They also suggested
using less thermally expansive concrete and increasing aggregate content by reducing more
thermally expansive cement paste content.
It should be noted that, GFRP bars are used mostly as internal reinforcement in lieu of steel
reinforcement to overcome the corrosion problem. GFRP bars are also composite materials
consist of continuous glass fibres in a polymer matrix (resin). Radial CTE of GFRP is higher
than the longitudinal CTE of GFRP as the radial CTE depends on resin and longitudinal CTE
depends on fibres. The coefficient of thermal expansion of GFRP is different from CTE of
concrete which may lead to thermal restraint stresses when subjected to temperature changes.
Especially radial CTE of GFRP may cause to such stress field in the surrounding concrete that
may lead to cracks along the bars in the concrete cover and consequently to bond failure (ISIS
Canada 2007).
2.8 FACTORS RELATED TO ENVIRONMENT
Bridge deck slabs are usually exposed to harsh environments such as freezing-thawing cycles,
temperature fluctuations and wetting-drying cycles within temperature and humidity ranges from
–40°C to +35°C and 30 to 100 %, respectively (Laoubi et al. 2006). Therefore, at early-ages,
Chapter 2: Literature Review
37
these structural elements may be subjected to different combinations of shrinkage and swelling.
Figure 2.9 shows the influence of three different curing environments on the magnitude of
shrinkage. It is believed that cracking tendency of concrete will increase with decreasing relative
humidity and increasing temperature and wind speed.
The effects of different environmental conditions on concrete cracking are discussed below. In
RC structures, damage due to severe environmental conditions can take various forms such as
reinforcement de-bonding, scaling, and micro cracking (Bishnoi 2004 and Alves et al. 2011).
Other forms of damage include large-scale spalling and crumbling of concrete and material
fatigue, resulting in loss of strength and stiffness.
2.8.1 Hot Weather
High temperature increases water demand for given workability and increased water content
increases drying shrinkage and thus increases the tendency of concrete cracking. The evaporation
rate of moisture from fresh concrete increases with increasing temperature and thus increases the
tendency of plastic shrinkage cracking (Koenigsfeld and Myers 2003). If the concrete placement
ambient temperature is higher, the hydration reaction reacts more rapidly and the rate of heat
evolutions is increased. Therefore, peak temperature of concrete is increased and thus the
tendency of concrete cracking increased as the concrete shrinks as it cools from the peak
temperature. Allowable maximum temperature during placement of concrete was suggested in
several studies. Krauss and Rogalla (1996) suggested maximum concrete placement temperature
of 27 °C (80 °F) and concrete temperature of at least 5-10 °C (41-50 °F) cooler than ambient
temperature. French et al. (1999) recommended placing concrete at maximum temperature of 32
°C (90 °F) and avoiding pouring concrete on days when temperature variation is greater than
approximately 10°C (50 °F). Xi et al. (2003) suggested, to avoid casting deck slabs when air
Chapter 2: Literature Review
38
temperature is higher than 27 °C (80 °F) and avoid large temperature variation during concrete
placement. For reinforced concrete elements with thickness of section less than 30 mm, the
allowable maximum temperature of the concrete as placed should be less than 35 °C (CSA
A23.1-09 2009).
9Fig. 2.9: The magnitude of shrinkage for Three Different Curing Environments (reproduced from
Holt and Leivo 2000).
2.8.2 Cold Weather
Frost damage to fresh concrete and slow gain in strength is the main problems of cold weather
concreting. Expansion of water (approximately below 4 °C water starts to expand) in fresh
concrete may suffer permanent damage. Slower setting time may be the problem of concrete
cracking as it allows greater evaporation while the concrete is plastic (Krauss and Rogalla 1996).
Xi et al. (2003) recommended avoiding casting deck slabs when the temperature is lower than
7.2 °C (45 °F), and maintaining concrete mix temperature above 10 °C (50 °F) for the first 72 hrs
and above 4 °C (40 °F) for the remaining curing period. French et al. (1999) suggested placing
Chapter 2: Literature Review
39
concrete deck slabs only where the ambient air temperature is above approximately 4 to 7 °C (40
to 45 °F). For reinforced concrete elements with thickness of section less than 30 mm, the
allowable minimum temperature of the concrete as placed should be more than 10 °C (CSA
A23.1-09 2009).
2.8.3 Relative Humidity
Drying and plastic shrinkage are the cause of loss of water from concrete and the magnitude of
water loss is due to the difference in relative humidity from the internal concrete to the external
environment. The ultimate shrinkage and rate of shrinkage of concrete will increase with
decreasing relative humidity as shown in Fig. 2.10 (ACI Committee 224 2001) and thus
increasing the cracking tendency of concrete.
2.8.4 Effect of Wind
High wind speed increases the evaporation rate and consequently plastic shrinkage crack. The
plastic shrinkage cracks occur when the rate of surface evaporation is higher than the bleeding
rate. Xi et al. (2003) recommended avoiding concrete placement when the evaporation rate is
above 1.0 kg/m2/hr. for normal concrete and 0.5 kg/m2/hr. for concrete with low water-cement
ratio. The use of fogging equipment and windbreaks were suggested in NCHRP Synthesis of
Highway Practice 333 (2004) to reduce the surface evaporation from fresh concrete. CSA (2014)
Standard A23.1-14 also suggested taking special protection to avoid plastic shrinkage cracking
when the rate of surface moisture evaporation exceeds 1.0 kg/m2/hr. Concrete mixtures with
pozzolans are susceptible for early-age cracking if the rate of evaporation exceeds 0.5 kg/m2/hr.
The rate of evaporation can be measured from Fig. 2.11 using measurements of air and concrete
temperature, wind velocity, and relative humidity close to the surface of the concrete.
Chapter 2: Literature Review
40
10Fig. 2.10: Shrinkage vs. Time for Different Relative Humidity (reproduced from ACI Committee
224 2001).
2.8.5 Effect of Freeze-Thaw Conditions
Further deterioration can occur due to expansion of absorbed moisture in FRP and concrete
under freeze-thaw cycling. In addition, freeze-thaw cycles can lead to degradation of the fiber-
matrix bond and further damage the fibers through local notching due to ice formation on their
surfaces (El-Badry et al. 2000). Temperature changes, due to difference in thermal properties
between FRP bars and surrounding concrete, can result in further damage to FRP-RC structures.
For example, GFRP can experience an expansion of 5-8 times greater than that of concrete in the
transverse direction due to temperature variations. This thermal incompatibility can cause de-
bonding of the bars from concrete under temperature changes (Gentry et al. 1999). Moreover,
under freeze/thaw cycles, ice formation at the FRP-concrete interface leads to damage of FRP-
concrete bond increasing existing crack width under sustained loads (Alves et al. 2011).
Chapter 2: Literature Review
41
2.8.6 Effect of Wet-Dry Conditions
Among the actions that may lead to variations in moisture content in concrete, the wet/dry cycle
is one of the aggressive environments suffered by concrete. Wetting-drying cycles are considered
critical in the durability-based design of concrete structures since volume changes due to
repetitive shrinkage/swelling may lead to material fatigue and de-bonding of reinforcement
(Zhang et al. 2012, Ayano et al. 2002).
2.9 FACTORS RELATED TO CONSTRUCTION PRACTICE
Different types of construction techniques have a significant effect on the early-age cracking of
concrete deck slabs. The effect of different construction practice factors are outlined below.
2.9.1 Curing
The water loss from concrete must be reduced to eliminate plastic shrinkage cracking and to
reduce drying shrinkage cracking. Therefore, effective curing is mandatory immediately after
proper finishing the surface of deck slabs. Almost all studies gave an emphasis on proper curing
to avoid early-age deck slabs cracking. Whiting et al. (2000) and Xi et al. (2003) recommended a
7-day continuous moist curing for concrete contains silica fume and/or fly ash to reduce early-
age cracking. After the 7-day wet curing period, application of curing compound was suggested
in NCHRP (2004) to decelerate the shrinkage and to improve the concrete properties.
Saadeghvaziri and Hadidi (2005) recommended the continuation of curing for a minimum of 7
consecutive calendar days immediately after finishing and to consider 14-day wet curing if
“early-open” is not an issue.
Chapter 2: Literature Review
42
2.9.2 Formwork
The effect of stay-in-place (SIP) forms on cracking appears inconsistent. Frosch et al. (2003)
have shown that additional restraint from stay-in-place forms can increase early-age cracking
tendency. However, Cheng and Johnson (1985) concluded that the use of SIP or timber forms
have negligible effect on early-age cracking in bridge deck slabs.
2.10 CRACK WIDTH
Concrete can provide an excellent first line of defense to keep internal reinforcement intact.
However, permeability and different types of cracking of concrete allow moisture and other
corrosive elements into the internal reinforcement causing deterioration of bond, strength of
internal reinforcement and strength of concrete itself (Gilbert 1992). Less permeable concrete is
obviously more durable when evaluated from the material point of view; but it may not always
be desirable or even essential to specify the lowest possible permeability for bridge deck slabs
when the bridge deck slabs crack. The increase in the number of cracks reduces the benefits of
the low permeability (high dens) concrete. As stated “We have managed to get excellent concrete
between the cracks” (Concrete Cracking Workshop 2005).
Though reinforcement cannot stop the crack, it can control the crack width. The finer the crack
width is the higher the durability. ACI Committee 224 (2001) limits the crack widths at the
tensile face of steel reinforced concrete structures for different exposure condition Table 2.5.
Chapter 2: Literature Review
43
11Fig. 2.11: The effect of concrete and air temperatures, relative humidity, and wind velocity on
rate of evaporation of surface moisture from concrete (reproduce from CSA/A23.1-14 2014).
5Table 2.5: Limits of crack widths for steel-reinforced structures (ACI Committee 224 2001)
Exposure Condition
Crack Width
in. mm
Dry air or protective membrane 0.016 0.41
Humidity, moist air, soil 0.012 0.30
De-icing chemicals 0.007 0.18
Seawater and seawater spray; wetting and drying 0.006 0.15
Water retaining structures 0.004 0.010
Chapter 2: Literature Review
44
As mentioned earlier, for lower stiffness of GFRP bars, lower internal tensile stress in concrete
will develop due to internal restraint from internal reinforcement against concrete shrinkage or
temperature variations and cause larger crack spacing followed by wider crack widths compared
to that of same steel reinforcement ratio (Chen and Choi 2002). Koenigsfeld and Myers (2003)
found three time larger crack widths for GFRP-RC specimens than specimens reinforced with
similar steel reinforcement ratio when subjected to restraint shrinkage. They also concluded that
twice as much GFRP reinforcement as steel is required to achieve similar crack control
characteristics when subjected to flexural loading. Though FRP do not corrode like conventional
steel re-bars, they are susceptible to deteriorate due to other degradation factors in potentially
aggressive environments and conditions such as thermal actions, alkali, salt, freeze-thaw actions,
ultraviolet rays; therefore, maximum crack width must be limited. Other than the aggressive
environmental conditions acceptable crack width limits include aesthetics and shear effect.
Canadian Standard Association (CSA 2006) limits the acceptable crack widths of 0.5 mm for
exterior exposure and 0.7 mm for interior exposure. ACI Committee 440 (2006) also
recommends using the crack width limitation of Canadian Standard Association (CSA 2006).
Chapter 3: Experimental Program
45
CHAPTER 3: EXPERIMENTAL PROGRAM
3.1 GENERAL
Based on literature, early-age cracking of concrete bridge deck slabs depends on various factors
related to concrete materials, structural design, environmental condition, and construction
practices. It is also found that transverse cracking in restrained bridge deck slabs is almost
inevitable no matter what precautions taken to minimize shrinkage. Therefore, control of crack
width and crack pattern is the main focus of this study by optimizing GFRP reinforcement ratio
and configuration subjected to different environmental conditions. This chapter includes design,
construction, and testing procedures of all eight test prototypes representing bridge deck slabs.
These specimens are categorised in two series. Series (I) consists of six slabs subjected to normal
laboratory conditions. Series (II) consists of two slabs subjected to freeze-thaw and wet-dry
cycling one week after casting.
3.2 MATERIAL PROPERTIES
3.2.1 Concrete
Normal-strength, ready-mixed concrete incorporating 13% silica fume by mass of binder (Table
3.1) with a target 28-day compressive strength of 40 MPa was used to provoke high tendency of
shrinkage as an extreme scenario that might be encountered in practice. The slump and fresh air
content of this concrete were in the ranges of 100-120 mm and 6±1%, respectively. The US-
Federal Highway Administration Guidelines [Silica fume user manual (Holland 2005)] reports
on the use of 4 to 15% silica fume in concrete for various infrastructure applications.
Chapter 3: Experimental Program
46
3.2.2 Reinforcements
Two different types of longitudinal reinforcement, steel and GFRP, were used in this study.
Sand-coated GFRP bars (Pultrall Inc. 2014) and deformed steel Grade 40 bars were used to
reinforce the slab prototypes in both layers (top and bottom). The GFRP bars are made of
continuous E-glass fibers with modified vinyl-ester resin with a fiber content of 75% by weigh
(Pultrall Inc. 2014). The mechanical properties of the GFRP reinforcement were obtained
according to the CSA S806-12 and ACI 440.3R-12 test specifications, while ASTM A370-14
standard method was used for the steel bars. The CSA/S806-12, Annex A (CSA 2012), provides
a new test method for measuring the gross cross-sectional area of FRP reinforcement (including
effective fibers and surface coating). According to the test specification, 8, 6, 3 and 1
specimen(s) with the same length of 290±0.5% mm were cut from the FRP bars No. 10, 13, 16
and 19, respectively. The average cross-sectional area of the bar equals to volume change
divided by length for the submerged GFRP bar in the cylindrical transparent container (glass or
plastic) (Eq. 3.1). The container has a dimension of 40 mm (internal diameter) and 300 mm
(height).
AFRP = 𝑣
𝑙× 1000 [Eq. 3.1]
where:
AFRP is the bar cross-sectional area (mm2), 𝑣 is the volume of the submerged GFRP bars (ml.),
and 𝑙 is the GFRP bars length (290 mm).
The longitudinal and transverse coefficients of thermal expansion for the used GFRP bars are 6.2
and 23.8 [×10-6
/°C], respectively, while the longitudinal and transverse coefficients of thermal
Chapter 3: Experimental Program
47
expansion for the steel bars used are 11.7 [×10-6
/°C]. Table 3.2 summarizes the mechanical
properties of the steel and GFRP bars used in this research.
6Table 3.1: Proportions of concrete per cubic meter
Ingredient Amount/m3
Cement Type GU* 365 kg
Coarse aggregate
(max. aggregate size, 20 mm)
1020 kg
Fine aggregate 650 kg
Air entraining agent 250 ml
Silica Fume 54.6 kg
Water 170 ml
*GU = General use.
7Table 3.2: Mechanical properties of sand-coated GFRP and steel bars
Bar type Bar
diameter
(mm)
Bar area (mm2) Modulus of
elasticity
(GPa)
Tensile
strength
(MPa)
Tensile
strain
(%) Nominal* CSA S806-12
Annex A
GFRP
No.10
9.5 71 170 65 1572 2.4
GFRP
No.13
12.7 127 197 65 1453 2.23
GFRP
No.16
15.9 198 291 62 1450 2.33
GFRP
No.19
19.1 285 394 63 1484 2.33
Steel
No. 15M
16 200 NA 200 fy* = 420 ɛy
* = 0.21
*fy: Steel yield strength, ɛy: Steel yield strain,
Chapter 3: Experimental Program
48
It should be noted that the nominal cross-sectional area of GFRP bars have been used to obtain
the reinforcement ratio and the mechanical properties of the bars.
3.3 EXPERIMENTAL PROGRAM
3.3.1 Characterization of the Concrete Mix
Concrete properties in terms of compressive and tensile strength, and modulus of elasticity were
measured at different ages. These tests were conducted based on the average value of five
standard cylinders of 100 × 200 mm for compressive strength and 150 × 300 mm for tensile
strength and modulus of elasticity tests at 3, 7, 14, 28 days after casting (Fig. 3.1). Also, the
concrete coefficient of thermal expansion was measured using three 76.2 × 152.4 mm cylindrical
samples at age 28 days. For each sample, metal reference disk were attached to the surface of the
sample using epoxy to identify three gauge lengths as shown in Fig. 3.2. The three gage lengths
are at 120 degrees apart. Each gage length measures 102 mm at room temperature (23 ºC). An
environmental chamber was used to cycle the temperature between +10 and +50 ºC. A dummy
sample was used to monitor the core temperature of the samples and ensure that the thermal
equilibrium was reached. A DEMEC gauge with 0.00254 mm accuracy was used to measure the
change in gage length with temperature change. Coefficient of thermal expansion was calculated
for the heating cycle from +10 to +50 ºC and for the cooling cycle from +50 to +10 ºC. The tests
were carried out based on the following test standard methods for each concrete batch to evaluate
the properties of the concrete:
Compressive strength tests (ASTM C 39/C 39M-03);
Modulus of elasticity test (ASTM C 469-02);
Tensile strength test (ASTM C 496/C 496M-04);
Chapter 3: Experimental Program
49
Concrete thermal deformation test (ASTM E831);
Creep coefficient tests (using formulas recommended by ACI 209.2R-08).
12Fig. 3.1: Casting test cylinders.
13Fig. 3.2: Coefficient of thermal expansion sample.
Chapter 3: Experimental Program
50
3.3.2 Test Setup and Prototypes
This study included eight full-size, cast-in-place deck slab prototypes, which were designed to
investigate the influence of reinforcement ratio and bar type (GFRP and steel) on transverse
early-age cracking in bridge deck slabs under different environmental conditions for a period of
112 days. The test slabs are divided into two series (Fig. 3.3). Series (I), which includes 6
specimens, is related to slabs investigating the effect of changing the longitudinal reinforcement
ratio and bar type subjected to shrinkage under laboratory conditions. Series (II), which includes
2 specimens, investigates the effect of freeze-thaw and wet-dry cycles on early-age cracking of
GFRP-RC bridge deck slabs. Series (I) consists of five end-restrained RC slabs (SG1, SG2, SG3,
SG4 and SS) and one unrestrained/unreinforced slab (F). The five RC slabs includes four GFRP-
RC slabs, SG1, SG2, SG3 and SG4, with four different GFRP reinforcement ratios of 0.3%,
0.5%, 0.7%, and 1.1%, respectively, in addition to one steel-RC slab (SS) with a reinforcement
ratio of 0.7%. Series (II) includes two slabs, G-FT and G-WD, reinforced with the minimum-
acceptable reinforcement ratio as obtained from series (I), which were tested under freeze-thaw
and wet-dry cycling conditions.
Figure 3.4 shows prototypes dimensions. According to CHBDC, (Clause 14.13.1.2), the
minimum allowable thickness of bridge deck slabs is 175 mm. Accordingly, in this study, a
thickness of 180 mm for all test slabs was selected. The full-size, cast-in-place concrete bridge
deck slabs (2500-mm long by 765-mm wide) of Series (I) and (II) were constructed and tested
under the normal laboratory conditions (Fig. 3.5) and environmentally controlled walk-in
chamber (Fig. 3.6), respectively. The effective width-to-length ratio was selected less than 1/3 to
ensure that the amount of shrinkage in the longitudinal direction is much more than that in the
transverse direction. In other words, there was three times as much concrete that tended to shrink
Chapter 3: Experimental Program
51
in the longitudinal direction than in the transverse direction. Consequently, a transverse crack is
expected to develop in order to relieve the larger tensile stress in the longitudinal direction. The
reinforcement configuration of the test specimens was selected based on the empirical design
method recommended by Section 16 of the CHBDC (Clause 16.8.8.1). According to this section,
the minimum FRP reinforcement ratio in the longitudinal bottom and top assemblies is 0.35%
with top and bottom covers equal to 35±10 mm (CHBDC, Clause16.4.4). All test prototypes had
similar top and bottom clear covers (25 and 30 mm, respectively) and a constant spacing of 255
mm for the longitudinal reinforcement (Fig. 3.4 (c)).
14Fig. 3.3: Schematic diagram for test matrix.
Chapter 3: Experimental Program
52
15Fig. 3.4: Deck slab dimensions (all dimensions are in mm): (a) side view, (b) top view, and (c)
cross-sections A-A
Chapter 3: Experimental Program
53
16Fig. 3.5: General view of the test setup and specimen under normal laboratory conditions (all
dimensions are in mm).
It is well documented in the literature (Nejadi and Gilbert 2004 and Saliba et al. 2011) that the
reduction in the cross section can force the main crack to occur at the well-instrumented location.
Therefore, in this study the cross section was reduced (notched) to 565 × 150 mm by steel
section attached to the forms to ensure that main cracking always occurs at this location (Fig.
3.7), which was depicted by experimental results.
3.3.3 Test Parameters
The effects of following parameters were studied on early-age cracking of RC bridge deck slabs
in this research (Table 3.3):
Chapter 3: Experimental Program
54
a) Longitudinal reinforcement ratio;
b) Longitudinal reinforcement material (GFRP and steel);
c) Different environmental conditions (wet-dry and freeze-thaw cycles).
For this study, the above parameters are implemented in the experiments as follows:
The results of slabs S1 and SG3 were used as control specimens (ρ = 0.7%) to investigate
the effect of different reinforcement material on early-age cracking.
Using the results of specimens SG1, SG2, SG3, and SG4 to study the effect of GFRP
reinforcement ratio with the similar bar spacing (different bar size) were investigated.
Specimen G-FT was subjected to freeze-thaw cycling after 7 days of casting for a period
of 105 days to evaluate optimum GFRP reinforcement ratio under freeze/thaw conditions.
Specimen G-WD was subjected to wet-dry conditions (after 7 days of casting) to
investigate the effect of wet/dry conditions on existing early-age cracking
3.3.4 Instrumentations
To measure strains in the GFRP bars in the vicinity of the first crack, three strain gauges were
attached to each bar at the top and bottom layers; one centered at the mid-span, and the other two
at 50 mm on each side as shown in Fig. 3.8. Two types of strain gauges were used: embedment
strain gauges (EGP series) in concrete and linear pattern strain gauges (20CBW series) on the
surface of concrete. For each slab, one strain gauge was embedded at the cracking (mid-span)
location. The other strain gauge was attached to the surface of concrete at an arbitrary distance of
270 mm (1.5 times slab thickness) away from the mid-span (cracking location) to avoid gauge
damage upon the occurrence of first cracking. The internal strain gauge was used to capture the
development of tensile strains within concrete up to failure by first cracking, while the surface
strain gauge measured the deformation of concrete in the vicinity of the cracking location during
Chapter 3: Experimental Program
55
the entire period of exposure. The width of the cracks developed was recorded throughout the
test using two PI-gauges. Also, the internal relative humidity was monitored by humidity sensors
embedded at the level of the reinforcement layers and mid-depth at an arbitrary distance of 625
mm away from the mid-span (cracking location) to avoid further stress concentration at cracking
place. All instrumentation was connected to a DAQ (data acquisition system) controlled by a
computer (Fig. 3.9).
17Fig. 3.6: General view of the test setup and specimen into the environmental chamber (all
dimensions are in mm).
Chapter 3: Experimental Program
56
18Fig. 3.7: Mid-length details.
8Table 3.3: Details of the parameters varied in the tests
Specimen
Bar Dia.
(mm)
Ar *
(mm2)
ρ
(%)
E×A
(kN)
ρprovided
ρmin
Temperature (°C)
SG1 9.5 285 0.30 18,525 0.4 20±2
SG2 12.7 508 0.5 33,020 0.7 20±2
SG3 15.9 791 0.7 49,042 1.0 20±2
SG4 19.1 1140 1.1 71,820 1.5 20±2
G-FT 15.9 791 0.7 49,042 1.0
frezze-thaw cycling applied
after 7 days of casting
G-WD 15.9 791 0.7 49,042 1.0
Wet-dry cycling applied after 7
days of casting
SS 16 800 0.7 160,000 1.2 20±2
F - - - - - 20±2
Ar*: Total area of 4 longitudinal bars (2 top and bottom)
Chapter 3: Experimental Program
57
3.3.5 Test Procedure
Prior to casting, the 2500-mm long slabs were effectively anchored at its ends by
1473×1000×1200 mm concrete blocks (Fig. 3.10), which were clamped (pre-stressed) to the
laboratory strong floor using 38-mm diameter dywidag-bars; then the inside surface of the
formwork was cleaned and thinly coated with a releasing agent (oil) to prevent adhesion of the
concrete (Fig 3.11).
The bottom surface of the slab was supported by three stay-in-place smooth, greasy plates (300
mm × 300 mm, spaced at 1250 mm as shown in Fig. 3.12) to reduce the effect of slab’s self-
weight on the reinforcement strains. For the first 24 hours after casting, a plastic tent was built
around the test prototypes and cylinders while electrical heaters were used to maintain the
internal concrete temperature at 35 °C without moist curing (Fig. 3.13).
Subsequently, the tent and formwork was removed, then PI-gauges were attached to the concrete
surface, and initial strain measurements were recorded. During the first 24 hours, the ambient
conditions around the slab (under tent) were 40 °C with 30-40% RH. In the meantime, the
average internal temperature and RH measured at the top reinforcement level were 35 °C and 90
%, respectively. After the tent was removed, the specimens were left in laboratory conditions
(20 ± 2 °C and 50-70 % RH) over 111 days. During that period the internal temperature at the
top reinforcement level was 20 ± 2 °C while the RH decreased from 95 to 70%. In order to
increase internal relative humidity (RH) for the slabs of Series (II) (G-FT and G-WD), water was
poured into the surface reservoir (approximately 5-mm thick) constructed by peripheral foam
dykes at the outer edge of the slabs G-FT and G-WD for freezing-thawing and wetting cycles
(Fig. 3.14).
Chapter 3: Experimental Program
58
Using the concrete cylinders (Fig. 3.15), the average compressive (ASTM C39M-03) and
splitting tensile (ASTM C496M-04) strengths and the modulus of elasticity (ASTM C469-02)
were obtained after 1, 3, 7, 14, 21 and 28 days (Table 3.4) to determine the development of
concrete properties (within a standard deviation of 10% from the average value).
3.3.6 Environmental Conditioning Schemes
3.3.6.1 Freezing-thawing cycles
Different freezing-thawing conditioning schemes had been used by researchers to study the
behaviour of RC elements externally or internally reinforced with FRP bars (Laoubi et al. 2006
and Alves et al. 2011). In this research, the temperature profile of Standard Test Method for
Resistance of Concrete to Rapid freezing-thawing (ASTM C-666 M-03 2008) was adopted. In
this standard, the freezing-thawing cycles consist of alternately lowering the temperature from
+4 to -18 ºC for freezing and raising it from -18 to +4 ºC for thawing. Thawing time should not
be less than 25% of the total freezing-thawing time. In order to reach the standard conditions in
the bottom reinforcement level of the slab, the applied freezing-thawing cycles consisted of
alternately decreasing the environmental chamber temperature from +22 to -25 ºC for freezing
and raising it from -25 to +35 ºC for thawing at a rate of 1.55 cycles/day to achieve the ASTM
temperature and duration requirements at the level of GFRP reinforcement. Figure 3.16 shows
the reading of thermocouples embedded in specimen G-FT at the level of bottom reinforcement
compared to the air temperature inside the chamber. Specimen G-FT was subjected to 163
freezing-thawing cycles over 105 days. Figure 3.17 indicates that ponded water (3-5 mm) on the
top of slab G-FT increased the average internal humidity to approximately 99% (i.e. beyond the
critical saturation level of 90%).
Chapter 3: Experimental Program
59
19Fig. 3.8: Typical instrumentation of deck slabs (all dimensions are in mm).
20Fig. 3.9: Measurement instruments; DAQ Amplifier, PI gauges, and Microscope.
Chapter 3: Experimental Program
60
21Fig. 3.10: Slab ends effectively held in position and restrained against translation.
22Fig. 3.11: Formwork is thinly coated with oil to prevent adhesion of the concrete.
Chapter 3: Experimental Program
61
23Fig. 3.12: Smooth supports at the bottom surface of the slabs to eliminate flexural action.
24Fig. 3.13: Temperature control during the first 24 hours.
Chapter 3: Experimental Program
62
25Fig. 3.14: Water was poured into the surface reservoir (for slabs G-FT and G-WD).
Chapter 3: Experimental Program
63
9
26Fig. 3.15: Equipment used in concrete material testing.
Table 3.4: Compressive, tensile and E-modulus test results for concrete under different environmental conditions
Ambient conditions N N N N D/W F/T N D/W F/T N D/W F/T
Property Age (days)
1 3 7 14 14 14 21 21 21 28 28 28
Compressive
Strength (MPa) 7±0.50 14±0.27 34±2.60 35±3.40 37±1.70 33±1.58 36±0.91 38±0.50 32±1.90 38±1.40 41±2.50 35±2.3
Tensile Strength
(MPa) 0.6±0.05 1.3±0.09 3.4±0.33 3.5±0.26 3.9±0.30 3.3±0.20 3.6±0.10 3.7±0.17 3.1±0.38 3.7±0.20 3.9±0.19 3.3±0.26
Modulus of
Elasticity (GPa) - 18±0.72 21.1±1.15 21.2±2.09 21.8±1.21 21.3±1.90 21.1±1.01 21.8±1.31 21.1±1.21 21.8±1.66 22.2±1.47 21±1.73
N: Normal laboratory conditions (22°C and 50 to 60% RH), D/W: Drying and wetting cycling (35°C to 22°C and 100 to 30 % RH respectively),
and F/T: Freeze-thaw cycling (-18 °C to +4 °C and 100% RH).
Chapter3: Experimental Program
64
27Fig. 3.16: A part of the freeze-thaw profile for specimen G-FT.
28Fig. 3.17: Relative humidity readings for the slab G-FT subjected to the freeze-thaw.
-30
-24
-18
-12
-6
0
6
12
18
24
30
36
42
29.0 29.5 30.0 30.5 31.0
Tem
per
atu
re °
C
Time(days) External G-FT-ρ = 0.7% Internal G-FT-ρ = 0.7%
60
65
70
75
80
85
90
95
100
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
RH
(%
)
Time ( days )
Core level Top Bar level Bot. Bar level
Chapter3: Experimental Program
65
3.3.6.2 Wetting-drying cycles
It should be noted that there are no standard test methods for the wetting-drying exposure of
concrete. The cyclic regime and the total number of cycles (five cycles) in this study were
selected similar to that adopted by Zhang et al. (2012) to achieve significant humidity changes at
the reinforcement level of the bridge deck slabs. Each wetting-drying cycle started with 14 days
of drying at 35±2 °C and 30% RH followed by 7 days of wetting at 22±2°C and 100% RH.
Figure 3.18 shows the reading of humidity sensors embedded in the test specimen at the different
levels of the cross section compared to the humidity in the chamber.
29Fig. 3.18: Relative humidity readings for the G-WD subjected to wet-dry exposure.
3.4 MICROSTRUCTURE TESTS
In additional to the early-age cracking of restrained concrete slabs exposed to harsh conditions,
they were vulnerable to material degradation especially at the mid-length (in the vicinity of the
crack) due to temperature and humidity variations. To capture this trend, three materials tests
Dynamic Modulus of Elasticity (DME), Rapid Chloride Permeability Test (RCPT), and
0
10
20
30
40
50
60
70
80
90
100
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
RH
(%
)
Time ( days )
Surface level Top Bar level Bot. Bar level
Chapter3: Experimental Program
66
Scanning Electron Microscopy (SEM) were conducted on cores extracted from the three GFRP-
RC slabs. A total of twelve 100-mm diameter cores were extracted; four cores for each slab
(close and away from left and right sides of the crack). All cores were extracted from slabs at the
end of the test period (112 days). For the DME test, full length cores were used while for the
other two tests, top 50-mm thick slices were cut from the cores extracted from different locations
in the slabs, as shown in the Fig. 3.19.
30Fig. 3.19: Taking cores from the slab.
Chapter3: Experimental Program
67
3.4.1 UPV Test
To determine the internal conditions of the cementitious matrix in terms of structural stiffness
and integrity, the dynamic modulus of elasticity (DME) was determined for all cores from the
ultrasonic pulse velocity (UPV) measurements (Fig. 3.20) according to ASTM C597 (2009).
31Fig. 3.20: UPV test machine.
According to the ASTM C597 specifications, DME test was performed based on the average
value of three pulse velocities, were measured, from the longitudinal direction of the cores
(cylinders) using the Eq. 3.1.
𝐸𝑑 =𝜗2𝜌(1+𝜇)(1−2𝜇)
(1−𝜇) Eq. 3.1
Where, Ed = Dynamic Modulus of Elasticity (DME) (GPa), ϑ = Pulse Velocity (PV) (m/s),
ρ = Concrete density (kg/m3), μ = Dynamic Poisson's ratio (assumed to be 1.5).
Chapter3: Experimental Program
68
3.4.2 Rapid Chloride Penetrability Test (RCPT)
To evaluate the interconnectivity of the pore structure in the concrete slabs after being subjected
to different environmental conditions, the rapid chloride penetrability test (RCPT) was performed
for the cores according to ASTM C1202 (2012) (Standard Test Method for Electrical Indication
of Concrete’s Ability to Resist Chloride Ion Penetration). The 50-mm thick discs were cut from
top layer of the cores as the test samples (Fig. 3.21). These discs were air-dried in the laboratory
for one hour and then their side surfaces were coated with rapid setting epoxy to reduce moisture
evaporation and leakage of solution during testing. Subsequently, the concrete discs were placed
in a vacuum desiccator under vacuum pressure for three hours.
32Fig. 3.21: Disks preparation for RCPT.
In the meantime, the required amount of water was boiled for de-aeration and allowed to cool
down to ambient temperature. After three hours of vacuuming, de-aerated water was allowed to
enter into the desiccator while the vacuum pump was still running. Subsequently, for additional
one hour, the vacuum pump was operated and then the valve was opened to allow air to enter
Chapter3: Experimental Program
69
into the desiccator. The specimens were kept in the desiccator and soaked under water for 18
hours before the actual test. On the following day, the concrete discs were put in the test cells,
where one compartment was filled with 3% NaCl solution (cathode) while the other
compartment was filled with 0.3 N NaOH solution (anode). During the test period (six hours), 60
V DC was applied to the cell compartments, while the temperature of sodium chloride solution
was continuously monitored by a thermocouple. The computer connected to the microprocessor
power supply recorded all the data during the entire test in terms of passing charges in Coulombs
through concrete to determine the penetrability class according to ASTM C1202 (Fig. 3.22).
33Fig. 3.22: RCPT test equipment.
After the RCPT, the specimens were axially split and sprayed with a silver nitrate solution,
which forms a white color in approximately 15 minutes, to measure the physical penetration
depth. The average depth of the white precipitate was determined at five different locations of
Chapter3: Experimental Program
70
each half specimen. This depth is considered to be an index of the ease of ingress of chloride
ions, and thus the connectivity/deterioration of the microstructure (Bassuoni et al. 2006).
3.4.3 Backscattered Scanning Electron Microscopy Test (BSEM)
To supplement the results of UPV and RCPT, the alteration of microstructure of concrete was
also assessed by backscattered scanning electron microscopy (BSEM) (Fig. 3.23) on thin
sections from cores extracted from G-FT and G-WD in the vicinity and away from the main
crack. The polished sections were prepared from fracture surfaces that were dried at 40°C for 24
h, impregnated with low-viscosity epoxy resin under pressure, cut, polished and carbon coated
(Fig. 3.24).
34Fig. 3.23: Backscattered scanning electron microscopy (BSEM).
Chapter3: Experimental Program
71
35Fig. 3.24: Typical prepared sample for the backscattered scanning electron microscopy (BSEM)
test.
Chapter4: Results and Discussion-laboratory Conditions
72
CHAPTER 4: RESULTS AND DISCUSSION - LABORATORY CONDITIONS
EFFECT OF REINFORCEMENT RATIO
4.1 GENERAL
It is documented that no experimental data is available for the minimum FRP reinforcement ratio
to control shrinkage and temperature cracking in FRP design codes and guidelines (CHBDC
2009, CSA/S806 12). Most of these codes and guidelines are based on modifying corresponding
formulas originally developed for steel bars and take into account the difference in properties and
behaviour between FRP and steel material. The objective of this chapter is to summarize the
experimental results for six full-scale of Series (I), which includes 6 full-scale slabs,
investigating the effect of changing the longitudinal reinforcement ratio (0.3, 0.5, 0.7 and 1.1%)
and bar type (steel) subjected to shrinkage under laboratory conditions. Also, one identical
restrained-free plain concrete slab was tested to measure the total free shrinkage strain of the slab
during the test period. The performance of the specimens is assessed and discussed in terms of
concrete cracking pattern, width, and spacing, and strains in the reinforcement and concrete. The
experimental results were compared with provisions of the CHBDC (CSA 2006) and predictions
from a published analytical model (Gilbert 1992) for estimating crack width of steel-RC
structures.
4.2 SLABS SUBJECTED TO LABORATORY CONDITIONS
4.2.1 General Observation
The width of cracks in the restrained slabs varied according to the environmental exposure and
different reinforcement material. While the magnitude of crack width depends on several factors
such as degree of restraint, quality of bond between concrete and reinforcement, size and
Chapter4: Results and Discussion-laboratory Conditions
73
distribution of bars, concrete quality and ambient conditions, the studied variables in this study
were the environmental conditions and reinforcement ratio and material. For each slab, the crack
width was considered as the average of the measured value at two locations across the slab width
at mid-span. Generally, the first crack in all specimens was observed within the first three days
after casting in the transverse direction before exposure. Figure 4.1 shows the cracking pattern
for all the slabs at the notched (mid-span) location. The cracks, which usually extended into the
full depth of slabs, typically occurred at mid-span (notched location). For the RC slabs, the bar
strain was presented as average strain readings of all instrumented bars (top and bottom) in the
vicinity of crack at mid-span. Prior to cracking the average strain level remained under 300 με.
The top and bottom reinforcement carried the full restraining force at each crack, while the stress
in the concrete was zero (Fig. 4.2). Once the crack formed at the mid-span, the strains increased
significantly. The internal concrete strain at cracking location was considered the embedment
concrete strain gauge reading before cracking, while due to damage of the internal gauge at
cracking time the surface concrete strain was presented using surface strain gauge 270 mm away
from the cracking location. Figures 4.2 shows the internal strain of the concrete at cracking, once
the early age cracks became visible for specimens SG1, SG2, SG3, SG4, and SS the measured
concrete internal tensile strains were 336, 315, 293, 213, and 212 με, respectively. For all
specimens after cracking, the concrete surface strain in the vicinity of the first crack changed to a
compressive strain. Once cracking occurred, the stiffness of slab in the vicinity of cracking
reduced depending on the reinforcement ratio and modulus of elasticity on either side of the
crack shortens elastically.
Chapter4: Results and Discussion-laboratory Conditions
74
36Fig. 4.1: Final crack pattern in the specimens.
37Fig. 4.2: Internal strain of concrete at cracking at cracking time.
Chapter4: Results and Discussion-laboratory Conditions
75
If the volumetric change of concrete due to shrinkage and thermal stresses is restrained, tensile
stresses will develop in concrete. If the induced tensile stresses are higher than the tensile
strength capacity of the concrete, the concrete will crack. Figure 4.3 represents that the total free
volumetric instabilities of free restraint slab F due to shrinkage under laboratory conditions was
171 μɛ at the end of test period. In this research increasing ambient temperature to 35 °C in the
first day after casting without moist curing followed by exposing the slabs to an air flow for 6
days, accelerated the amount of shrinkage to 159 μɛ within first week.
4.2.2 Characteristics of cracks
4.2.2.1 Slab SG1
Figure 4.4 shows the change in crack width of the Specimen SG1 over 112 days. The first crack
occurred for Slab SG1 within 31 hours. Primarily, the width of a crack in a restrained slab varied
depending on the bonded reinforcement ratio and material crossing the crack. In the slab SG1 (ρ
= 0.3%) the crack width reached the allowable value of 0.5 mm (ACI 440 2006, CSA 2006) after
40 hours. This crack width grew to 0.73 mm after 112 days test period.
4.2.2.2 Slab SG2
The first crack occurred for SG2 within 37 hours. Fig. 4.5 shows the change in crack width over
112 days. For slab SG2 (ρ = 0.5%) the crack width reached the allowable value of 0.5 mm (ACI
440 2006, CSA 2006) after 42 hours. This crack width grew to 0.64 mm after 112 days.
4.2.2.3 Slab SG3
For Slab SG3 the first crack occurred for slabs SG3 within 48 hours. Figure 4.6 represents the
change in crack width over 112 days. The final crack width for slabs SG3 (ρ = 0.7%) was 0.33
mm (lower that 0.5 mm recommended by CHBDC) after 112 days of exposure to laboratory
Chapter4: Results and Discussion-laboratory Conditions
76
conditions, in the next phase of the experimental works, to assess the effect of different
environmental conditions on early age cracking the slab SG3 (ρ = 0.7%) is selected as slab with
optimum reinforcement ratio.
4.2.2.4 Slab SG4
Figure 4.7 shows the change in crack width for specimen SG4 over 112 days. For this slab the
first crack occurred within 55 hours. The final crack widths grew to 0.24 mm (lower that 0.5 mm
recommended by ACI 440 2006, CSA 2006) after 112 days. Further volumetric instability in the
slab SG4 causes second and third cracks occurred at 63 days of casting on both sides of the first
crack. While additional shrinkage in slabs SG1 to SG3 increases the crack width. An increase in
the GFRP reinforcement ratio leads to less stiffness reduction at first cracking (at mid-span), thus
the restraining force after cracking remains high and the stress in bars is low. Therefore with a
high restraining force, due to future drying shrinkage or any environmental temperature
variation, the concrete in regions away from the first crack tends to experience further cracking.
4.2.2.5 Slab SS
Figure 4.8 illustrates the change in crack width over 112 days. The first crack occurred for slab
SS within 58 hours. For this slab (reinforced with steel ρ = 0.7%) the final crack widths grew to
0.18 mm after 112 days. Further shrinkage and higher cross-section stiffness at cracking location
due to higher modulus of elasticity of steel-reinforcement (Es = 200 GPa) compared with the
same GFRP-reinforcement ratio (EGFRP = 62 GPa) causes second and third cracks occurred at 19
days of casting on both sides of the first crack. While additional shrinkage in slab SG3 increases
the crack width. An increase in the reinforcement modulus of elasticity leads to less stiffness
reduction at first cracking (at mid-span), thus the restraining force after cracking remains high
and the stress in bars is low. Therefore with a high restraining force, due to future drying
Chapter4: Results and Discussion-laboratory Conditions
77
shrinkage or any environmental temperature variation, the concrete in regions away from the first
crack tends to experience further cracking.
38Fig. 4.3: Total free shrinkage of the plain concrete slab F.
39Fig. 4.4: Development of crack width with time (slab SG1).
0
30
60
90
120
150
180
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time (days)
Free plain Concrete Strain
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Cra
ck W
idth
(m
m)
Time (days)
SG1-ρ = 0.3%
Permissible crack width for FRP RC structures according to CHBDC
Chapter4: Results and Discussion-laboratory Conditions
78
40Fig. 4.5: Development of crack width with time (slab SG2).
41Fig. 4.6: Development of crack width with time (slab SG3).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Cra
ck W
idth
(m
m)
Time (days)
SG2-ρ = 0.5%
Permissible crack width for FRP RC structures according to CHBDC
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Cra
ck W
idth
(m
m)
Time (days)
SG3-ρ = 0.5%
Permissible crack width for FRP RC structures according to CHBDC
Chapter4: Results and Discussion-laboratory Conditions
79
42Fig. 4.7: Development of crack width with time (slab SG4).
43Fig. 4.8: Development of crack width with time (slab SS).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Cra
ck W
idth
(m
m)
Time (days)
SG4-ρ = 1.1%
Permissible crack width for FRP RC structures according to CHBDC
Second and thrid Cracks
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Cra
ck W
idth
(m
m)
Time (days)
SS-ρ = 0.7%
Second and third Cracks
Chapter4: Results and Discussion-laboratory Conditions
80
4.2.3 Tensile Strains in Reinforcement
4.2.3.1 Slab SG1
Prior to cracking the average strain level remained under 100 με, but once crack formed at the
mid-span, for specimen SG1 the average strain in reinforcement increased promptly to 3000 με,
while the strain away from the cracking location was still less than 300 με. Figure 4.9 shows the
average strain readings of all instrumented bars (top and bottom) in the vicinity of crack at mid-
span. For slab SG1, the final average strains reached to 3750 με at the end of test period.
4.2.3.2 Slab SG2
Figure 4.10 illustrates the average strain readings of all instrumented bars (top and bottom) in the
vicinity of crack at mid-span. Prior to cracking the average strain level remained under 100 με,
but once crack formed at the mid-span, for specimen SG2 the average strain in reinforcement
increased promptly to 1900 με, while the strain away from the cracking location was still less
than 300 με. In the slab SG2 the final average strains was 2480 με after 112 days.
4.2.3.3 Slab SG3
For specimen SG3 prior to cracking the average reinforcement strain was less than 100 με, once
crack formed this value jumped to 1450 με in the notched location. The average strain level
location was still less than 300 με away from the cracking location. Figure 4.11 illustrates the
average strain readings of all instrumented bars (top and bottom) in the vicinity of crack at mid-
span. For slab SG3 the final average strains reached to 1520 με after 112 days.
4.2.3.4 Slab SG4
Prior to cracking the average strain level remained under 100 με, but once crack formed at the
mid-span, for specimen SG4 the average strain in reinforcement increased promptly to 1240 με,
Chapter4: Results and Discussion-laboratory Conditions
81
while the strain away from the cracking location was still less than 300 με. Figure 4.12 illustrates
the average strain readings of all instrumented bars (top and bottom) in the vicinity of crack at
mid-span. The final average strains (after 112 days) were 1005 με for slab SG4. Second and third
62 days after casting causes the average reinforcement strain drops to 1000 με (strain changes
=186 με). This behaviour can be attributed to higher cross-section stiffness at cracking location
in the slab with higher reinforcement ratio (ρ = 1.1%) compared with slabs SG1 (ρ = 0.3 %) to
SG3 (ρ = 0.7%). While additional shrinkage in slabs SG1 to SG3 increases the crack width.
4.2.3.5 Slab SS
Prior to cracking the average strain level remained under 100 με, but once crack formed at the
mid-span, for specimen SS the average strain in reinforcement increased promptly to 680 με,
while the strain away from the cracking location was still less than 300 με. Figure 4.13 illustrates
the average strain readings of all instrumented bars (top and bottom) in the vicinity of crack at
mid-span. The final average strains (after 112 days) were 410 με for slab SG4. Second and third
19 days after casting causes the average reinforcement strain drops to 580 με (strain changes
=107 με). Further shrinkage and higher cross-section stiffness at cracking location due to higher
modulus of elasticity of steel-reinforcement (Es=200 GPa) compared with the same GFRP-
reinforcement ratio (EGFRP=62 GPa) causes second and third cracks occurred at 19 days of
casting on both sides of the first crack.
4.2.4 Concrete Surface Strain
4.2.4.1 Slab SG1
Figure 4.14 shows the surface strains of concrete in the vicinity of the first crack. Once cracking
occurred, the stiffness of slab in the vicinity of cracking reduced depending on the reinforcement
Chapter4: Results and Discussion-laboratory Conditions
82
ratio and the concrete on either side of the crack shortens elastically. After cracking, the concrete
surface strain in the vicinity of the first crack changed to a compressive strain (negative values in
Fig. 4.14). In the specimen SG1, as the concrete shrunk the measured surface strains increased to
525 με.
4.2.4.2 Slab SG2
Once concrete surface tensile stress exceeds concrete tensile strength cracking occurred (Fig.
4.15), at this point the stiffness of slab in the vicinity of cracking reduced depending on the
reinforcement ratio and the concrete on either side of the crack shortens elastically. After
cracking, the concrete surface strain in the vicinity of the first crack changed to a compressive
strain (negative values in Fig. 4.15). As the concrete shrunk, the measured surface strains
decreased to 490 με.
4.2.4.3 Slab SG3
Figure 4.16 shows the surface strains of concrete of the slab SG3 in the vicinity of the first crack.
As the concrete shrunk, the measured surface strains reached to 290 με. Once cracking occurred,
the stiffness of slab in the vicinity of cracking reduced depending on the reinforcement ratio and
the concrete on either side of the crack shortens elastically. For SG3 after cracking, the concrete
surface strain in the vicinity of the first crack changed to a compressive strain (negative values in
Fig. 4.16).
4.2.4.4 Slab SG4
The surface strains of concrete in the vicinity of the first crack for slab SG4 is shown in Fig.
4.17. In slab SG4, after cracking, the concrete surface strain in the vicinity of the first crack
changed to a compressive strain (negative values in Fig. 4.17). Once cracking occurred, the
Chapter4: Results and Discussion-laboratory Conditions
83
stiffness of slab in the vicinity of cracking reduced depending on the reinforcement ratio and the
concrete on either side of the crack shortens elastically. In this specimen, as the concrete shrunk,
the measured surface strains were 216 με after 112 days.
4.2.4.5 Slab SS
Figure 4.18 shows the surface strains of the concrete in the vicinity of the first crack. Once
cracking occurred, the stiffness of slab in the vicinity of cracking reduced depending on the
reinforcement ratio and the concrete on either side of the crack shortens elastically. In the slab
SS after cracking, the concrete surface strain in the vicinity of the first crack changed to a
compressive strain (negative values in Fig. 4.18). In the slab SS, as the concrete shrunk, the
measured internal tensile strains increased to 215 με.
44Fig. 4.9: Average reinforcement strain (Top and Bot.) at cracking (slab SG1).
0
1000
2000
3000
4000
5000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SG1-ρ = 0.30%
Chapter4: Results and Discussion-laboratory Conditions
84
45Fig. 4.10: Average reinforcement strain (Top and Bot.) at cracking (slab SG2).
46Fig. 4.11: Average reinforcement strain (Top and Bot.) at cracking (slab SG3).
0
1000
2000
3000
4000
5000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SG2-ρ = 0.50%
0
1000
2000
3000
4000
5000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SG3-ρ = 0.70%
Chapter4: Results and Discussion-laboratory Conditions
85
47Fig. 4.12: Average reinforcement strain (Top and Bot.) at cracking (slab SG4).
48Fig. 4.13: Average reinforcement strain (Top and Bot.) at cracking (slab SS).
0
1000
2000
3000
4000
5000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SG4-ρ = 1.1%
Second and third crack
0
1000
2000
3000
4000
5000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
Series5
Second and third Cracks
Chapter4: Results and Discussion-laboratory Conditions
86
49Fig. 4.14: Surface strains of concrete in the vicinity of the first crack (SG1).
50Fig. 4.15: Surface strains of concrete in the vicinity of the first crack (SG2).
-700
-600
-500
-400
-300
-200
-100
0
100
200
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SG1-ρ = 0.3%
-700
-600
-500
-400
-300
-200
-100
0
100
200
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SG2-ρ = 0.5%
Chapter4: Results and Discussion-laboratory Conditions
87
51Fig. 4.16: Surface strains of concrete in the vicinity of the first crack (slab SG3).
52Fig. 4.17: Surface strains of concrete in the vicinity of the first crack (slab SG4).
-700
-600
-500
-400
-300
-200
-100
0
100
200
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SG3-ρ = 0.7%
-700
-600
-500
-400
-300
-200
-100
0
100
200
0 10 20 30 40 50 60 70 80 90
Str
ain
(μ
ɛ)
Time(days)
SG4-ρ = 1.1%
Chapter4: Results and Discussion-laboratory Conditions
88
53Fig. 4.18: Surface strains of concrete in the vicinity of the first crack (slab SS).
4.3 DISCUSSION OF SLABS UNDER NORMAL LABORATORY CONDITIONS
4.3.1 Crack Characteristics
Primarily, the width of a crack in a restrained slab varied depending on the bonded reinforcement
ratio crossing the crack. Although, the magnitude of crack width depends on several factors such
as degree of restraint, quality of bond between concrete and reinforcement, size and distribution
of bars and the concrete quality; the only variable in this study was the bar size (reinforcement
ratio). For slab SG1 (ρ = 0.3%) and SG2 (ρ = 0.5%) the crack width reached the allowable value
of 0.5 mm (ACI 440 2006, CSA 2006) after 40 and 42 hours, respectively (Fig. 4.19). These
crack widths grew to 0.73 and 0.64 mm after 112 days, respectively. For slabs SG3 (ρ = 0.7%),
SG4 (ρ = 1.1%), and S (RC with steel ρ = 0.7%) the final crack width were 0.33, 0.24, and 0.18
mm, respectively, after 112 days of exposure to laboratory conditions. Generally, an increase in
the GFRP reinforcement ratio caused reduction of crack width and average crack spacing. Also
-700
-600
-500
-400
-300
-200
-100
0
100
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
SS-ρ = 0.70%
Chapter4: Results and Discussion-laboratory Conditions
89
the final crack width in the slab SG1 was 0.33 mm, while in the specimen with the similar
reinforcement ratio of steel (SS) final crack width reached to 0.18 mm after 112 days of exposure
to normal laboratory conditions. It was expected due to lower section stiffness of the GFRP-RC
slab compare to the steel-RC slab. As the reinforcement ratio and modulus of elasticity increased
from 0.3% to 1.1%, and 62 GPa to 200 GPa respectively, the average crack spacing reduced
from 2500 mm to 625 mm. In the specimens SG1, SG2, SG3, reinforced with equals or lower
than minimum reinforcement ratio recommended by CHBDC, the crack spacing was 2500 mm
while in the in Slab SG4, and SS the second and third crack occurred after 63 and 19 days of
casting, respectively on both sides of the first crack, resulting in a reduced crack spacing of 625
mm. An increase in the GFRP reinforcement area or reinforcement modulus of elasticity leads to
less stiffness reduction at first cracking (at mid-span), thus the restraining force after cracking
remains high. With a high restraining force, due to future drying shrinkage or any environmental
temperature variation, the concrete in regions away from the first crack tends to experience
further cracking.
Prior to cracking the average strain level in the reinforcement in the vicinity of the crack
remained under 100 με, but once crack formed at the mid-span, for specimens SG1, SG2, SG3,
SG4, and SS the average strain in reinforcement increased promptly to 3000, 1900, 1450, 1130,
and 685 με, respectively, while the strain away from the cracking location was still less than 300
με.
The average strain decreased with increasing the reinforcement ratio or modulus of elasticity.
The final average strains (after 112 days) were 3750, 2480, 1520, 1005, and 410 με for SG1,
SG2, SG3, SG4, and SS, respectively (Fig. 4.19). After the first cracking in specimens with
higher reinforcement ratios or higher modulus of elasticity, subsequent shrinkage caused further
Chapter4: Results and Discussion-laboratory Conditions
90
gradual increases in the restraining force, and hence in the concrete stress away from the crack.
In slab SG4 (reinforced with the highest reinforcement ratio), and SS (reinforced with steel
reinforcement) second and third cracks were developed 62, and 19 days respectively, after
casting. Comparatively, in the specimens reinforced with the minimum or lower GFRP
reinforcement ratios, additional shrinkage only increased the crack width without forming new
cracks. This is because the concrete was no longer fully restrained, due to the lower stiffness of
the slab at the first crack.
54Fig. 4.19: The final crack width and average reinforcement strain (Top and Bot.) at cracking
location.
4.3.2 Strains in Concrete
The test results indicate that the deformation of concrete decreased with increasing the
reinforcement ratio. In specimens SG1, SG2, SG3, SG4 and SS as the concrete shrunk, the
measured internal tensile strains 135, 126, 96, 76 and 60 με, respectively. Internal strains of
concrete were higher since the gauges were located at the mid-span (notched section under the
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-1000
0
1000
2000
3000
4000
5000
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20
Str
ain
(μ
ɛ)
Reinforcement ratio (%)
Reinforcement strain Crack widthC
rack
wid
th
(m
m)
Chapter4: Results and Discussion-laboratory Conditions
91
maximum tensile stress); while surface strains showed lower value as the gauges were placed
away from the mid-span location, where the tensile stress is reduced. With increasing the
reinforcement ratio from 0.3 to 1.1%, the internal and surface strain of concrete reduced by
approximately 74 and 53%, respectively. For SG1, SG2, SG3, SG4 and SS after cracking, the
concrete surface strain in the vicinity of the first crack changed to a compressive strain (negative
values in Fig. 4.14 to 4.18). Once cracking occurred, the stiffness of slab in the vicinity of
cracking reduced depending on the reinforcement ratio and the concrete on either side of the
crack shortens elastically.
4.4 THEORETICAL VS. EXPERIMENTAL RESULTS
Limited studies provided formulas to predict cracking characteristics of RC deck slabs and stress
distribution in bars at cracking locations due to restrained shrinkage. In this section, the
experimental results from this study are compared to predictions from a theoretical model for
steel-RC restrained members that are not subjected to significant bending (Gilbert 1992). In his
theoretical analysis, Gilbert (1992) explained that shrinkage causes an axial force built-up (Eq. 1)
in restrained members, which leads to direct tension cracks. He proposed Eqs. 4.2 and 4.3 to
calculate the stress in the bars, in the vicinity of the crack, and the crack width, respectively. In
this model, the restraint is provided to the longitudinal movement caused by shrinkage and
temperature changes. The results indicate that as these equations were developed for steel-
reinforced members, modification factors would be needed for the equations to be applicable to
FRP-reinforced slabs. Table 4.1 illustrates input values for parameters using in equations 4.1 to
4.3.
Chapter4: Results and Discussion-laboratory Conditions
92
𝑁(∞) =−3𝐴𝑠𝑛
∗𝐸𝑠∆𝑢
2𝑠0𝑚−(3𝐿−2𝑠0𝑚)𝑛
∗𝐴𝑠
2𝑠0𝑚(𝜎𝑎𝑣 + 𝜀
∗𝑠ℎ𝐸
∗𝑒) [Eq. 4.1]
𝜎∗𝑠2 =𝑁(∞)
𝐴𝑠 [Eq. 4.2]
𝑤 = −[𝜎∗𝑐1
𝐸∗𝑒(𝑠 −
2
3𝑆0) + 𝜀
∗𝑠ℎ𝑆] [Eq. 4.3]
where N(∞), As, ES, ∆𝑢, S0, m, 𝜎𝑎𝑣, 𝜀∗𝑠ℎ and 𝐸∗𝑒 are final restraining tensile force, reinforcement
bar area (mm2), modulus of elasticity of re-bars (MPa), support displacement (mm), correction
factor, concrete average stress (MPa), final shrinkage and effective concrete modulus of
elasticity (MPa), respectively. Also, 𝜎∗𝑠2, w, 𝜎∗𝑐1 and S are final reinforcement stress (MPa),
crack width (mm), concrete final stress (MPa) and crack spacing (mm), respectively.
10Table 4.1: Input data for parameters used in equations 4.1 to 4.3
Slab
AGFRP
(mm2)
db
(mm)
ε*sh
EGFRP
(MPa)
Ft (GFRP)
(MPa)
∆u
(mm)
SG1 284 9.5 -3.09e-4 65351 1572 0.031
SG2 508 12.7 -3.09e-4 65607 1759 0.035
SG3 764 15.9 -3.09e-4 62297 1725 0.037
SG4 1140 19.1 -3.09e-4 63374 1484 0.04
l = 2500 mm, t = 180 mm, ϕ* = 0.6, ft (7) = 3.4 MPa, fc(3) = 25, fc(28) = 38 MPa, Ec(3) = 20200 MPa, Ec(28) =
21800 MPa
Considering the fully restrained member in direct tension as the concrete shrinks, the restraining
force gradually increases until the first crack occurs, which is usually within two days from the
commencement of drying. Immediately after the first cracking, the restraining force reduces and
the concrete stress away from the crack is less than the tensile strength of the concrete. The
Chapter4: Results and Discussion-laboratory Conditions
93
concrete on either side of the crack shortens elastically and the crack opens to a width w. At the
crack location, the reinforcement carries the entire force. In the region immediately adjacent to
the crack the concrete and the reinforcement stresses vary considerably, and a region of partial
bond breakdown exists. At a distance So from the crack, which was earlier proposed by Favre et
al. (1983) for a member containing deformed bars or welded wire mesh (Eq. 4.1), the concrete
and the reinforcement stresses are no longer influenced directly by the presence of the crack. It
was suggested that the value of so to be multiplied by 1.33 to achieve better predictions for RC
member with steel bars (Gilbert 1992). In this study, a coefficient of 1.33 for so led to significant
discrepancy between the model’s predictions and experimental data. Hence, the coefficient value
was varied from 0.1 to 1.6 in 0.1 increments until a reasonable agreement (relatively smaller
error) was observed between the two data sets; this was obtained at a coefficient of 0.7. The
equation used to calculate the error is given by:
𝑒 =𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 [Eq. 4.4]
Figure 4.20 shows a comparison between the maximum calculated final crack width (obtained
using the analytical model developed by Gilbert 1992) and the maximum average of those
observed in the laboratory. The measured width of shrinkage cracks, agrees with the results of
the analytical model with an error of approximately 6.8%.
Chapter4: Results and Discussion-laboratory Conditions
94
55Fig. 4.20: Experimental and theoretical results for the final crack width.
Comparisons between the theoretical and experimental results for the final stress in the GFRP
bars in the vicinity of cracking are presented in Fig. 4.21. Except for slab SG1, the measured
stress, agree with the results of the analytical model with a 10% error. The discrepancy between
theoretical and experimental results of SG1 for stress value on the GFRP bars was due to the
effect of small GFRP bar diameter on the bond-slip relationship between reinforcement and the
surrounding concrete at cracking location.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SG1-ρ = 0.30% SG2-ρ = 0.50% SG3-ρ = 0.70% SG4-ρ = 1.1%
Experimental Theoretical (Coeff. = 1.33) Theoretical (Coeff. = 0.7)
Reinforcement Ratio (%)
Cra
ck W
idth
(m
m)
e:error
e ~0.15%
e ~1.7% e ~10.3%
e ~1.02%
e ~9.34% e ~2.5%
e ~6.8%
Permissible crack width for FRP-RC structures
according to CHBDC
e ~1.9%
Chapter4: Results and Discussion-laboratory Conditions
95
56Fig. 4.21: Final experimental and theoretical results for the final stresses in GFRP bars at
cracking.
0
50
100
150
200
250
300
350
400
SG1-ρ = 0.30% SG2-ρ = 0.50% SG3-ρ = 0.70% SG4-ρ = 1.1%
Experimental Theoretical (Coeff. = 1.33) Theoretical (Coeff. = 0.7)
Reinforcement Ratio (%)
Str
ess
(MP
a)
e ~10% e ~75%
e ~48%
e ~49%
e ~2%
e ~57% e ~52%
e ~2%
Chapter5: Results and Discussion-environmental Conditions
96
CHAPTER 5: RESULTS AND DISCUSSIO - EFFECT OF ENVIRONMENTAL
CONDITIONS
5.1 GENERAL
The current chapter reports the test results and the observations of Series (II) including two
specimens subjected to harsh environmental conditions. The objective of the second series was to
evaluate the effect of freeze-thaw and wet-dry cycling on the development of early-age cracking
on the G-FT and G-WD bridge deck slabs reinforced with GFRP reinforcement. The two
specimens of this series are reinforced with the minimum-acceptable reinforcement ratio as
obtained by first series. All specimens are properly instrumented to monitor strains, humidity,
and temperature history. The performance of the specimens is assessed and discussed in terms of
concrete weight loss, cracking pattern, width, and spacing, and strains in the reinforcement and
concrete. The experimental results were compared with provisions of the CHBDC (CSA 2006).
5.2 GENERAL OBSERVATIONS
The width of cracks in the restrained slabs varied according to the environmental exposure and
different reinforcement material. While the magnitude of crack width depends on several factors
such as degree of restraint, quality of bond between concrete and reinforcement, size and
distribution of bars, concrete quality and ambient conditions, the studied variables in this study
were the effect of different environmental conditions on the slabs reinforced with minimum-
acceptable reinforcement ratio subjected to shrinkage (as obtained by series (I)). For each slab,
the crack width was considered as the average of the measured value at two locations across the
slab width at mid-span. Generally, the first crack in all specimens was observed within the first
Chapter5: Results and Discussion-environmental Conditions
97
three days after casting in the transverse direction before exposure. Figure 5.1 shows the
cracking pattern for all the slabs at the notched (mid-span) location. The cracks, which usually
extended into the full depth of slabs, typically occurred at mid-span (notched location). For the
RC slabs, the bar strain was presented as average strain readings of all instrumented bars (top
and bottom) in the vicinity of crack at mid-span. Prior to cracking the average strain level
remained under 300 με. The top and bottom GFRP reinforcement carried the full restraining
force at each crack, while the stress in the concrete was zero (Fig. 5.2). Once the crack formed at
the mid-span, the strains increased significantly. The internal concrete strain at cracking location
was considered the embedment concrete strain gauge reading before cracking, while due to
damage of the internal gauge at cracking time the surface concrete strain was presented using
surface strain gauge 270 mm away from the cracking location. Figures 5.2 shows the internal
strain of the concrete at cracking, once the early age cracks became visible for specimens G-FT
and GWD the measured concrete internal tensile strains were 276 and 310 με, respectively. For
all specimens after cracking, the concrete surface strain in the vicinity of the first crack changed
to a compressive strain. Once cracking occurred, the stiffness of slab in the vicinity of cracking
reduced depending on the reinforcement ratio and modulus of elasticity on either side of the
crack shortens elastically.
5.3 FREEZE-THAW EXPOSURE
The behavior of restrained concrete elements under freezing-thawing conditions is affected by
multiple variables (e.g. internal water expansion, and material contraction due to low
temperature). It is well documented that if concrete elements are critically saturated (internal RH
> 90%), the water volume expansion phenomenon in larger capillary pores induces considerable
volume changes of concrete during freezing. At the onset of ice crystallization, the frictional
Chapter5: Results and Discussion-environmental Conditions
98
resistance to ice growth creates internal pressure in the pores leading to concrete expansion
(Scherer et al. 2002). In addition, ice formation in the void space imbibes water from the smaller
(gel) pores, creating negative (suction) pressure in the matrix and thus contraction (Towers and
Helmuth 2008). Hence, the total volume change of concrete is a combination of expansion and
contraction from hydraulic and osmotic pressures (Fig. 5.3).
57Fig. 5.1: Final crack pattern in slabs G-FT and G-WD.
58Fig. 5.2: Internal strain of concrete at cracking at cracking time.
Chapter5: Results and Discussion-environmental Conditions
99
59Fig. 5.3: Schematic of approximations of pore geometry in concrete.
The transverse full-depth crack occurred for slab G-FT within 47 hours (before exposure) at the
mid-length (notched section). Figure 5.4 shows the change in crack width in this slab over 163
freezing-thawing cycles (112 days).
Crack width reached to its maximum and minimum point at +4 °C (thawing) and -18 °C
(freezing), respectively, in each cycle. At the last cycle (163), the crack width varied between
0.29 and 0.42 mm corresponding to the freezing-thawing stages, respectively (Fig. 5.5). The
lower crack width recorded during freezing periods can be attributed to the volumetric expansion
of the critically saturated slab, which led to partial closure of the crack opening. Upon relieving
the expansion pressure during thawing periods, the crack width increased up to 0.42 mm (in the
Chapter5: Results and Discussion-environmental Conditions
100
last cycle), which is 40 and 27% higher than the crack width measured before the freezing-
thawing exposure and in the normal exposure (slab SG3), respectively.
60Fig. 5.4: Crack width development in the specimen under freeze-thaw conditions.
61Fig. 5.5: Crack width development in the slab G-FT under freeze-thaw conditions during the last
cycle.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Cra
ck W
idth
(m
m)
Time (days)
0.20
0.30
0.40
0.50
0.60
-25 -20 -15 -10 -5 0 5 10
Cra
ck w
idth
(mm
)
Temprature (ºC)
Last cycle (163)-G-FT-ρ = 0.7%
Permissible crack width for FRP-RC structures according to CHBDC
Permissible crack width for FRP-RC structures according to CHBDC
Chapter5: Results and Discussion-environmental Conditions
101
For slab G-FT, Fig. 5.6 shows the average fluctuation of the strains in the reinforcement at
cracking after 163 freezing-thawing cycles. In the last cycle, the strains of the reinforcement at
the cracking location were 1020 and 1690 με during the freezing-thawing stages, respectively
(Fig. 5.7). Complying with the crack width results, this trend is attributed to the repetitive
volumetric change associated with frost action as discussed earlier.
Also, it was observed that slab G-FT suffered from moderate surface scaling (Fig.5.8). Figure 5.9
indicates surface scaling less than 0.5 kg/m2 at the end of exposure (BNQ 2002), which is a
typical damage manifestation of concrete exposed to freezing-thawing cycles. This trend might
be ascribed to over finishing the surface of slab G-FT, which led to reducing the volume of air
entrainment in the surface as shown by the Scanning Electron Microscopy (SEM) analysis.
5.4 WETTING AND DRYING EXPOSURE
Wetting-drying conditions may significantly affect RC elements due to the variation of moisture
distribution with depth and accelerated shrinkage during drying periods. For slab G-WD, the
relative humidity of the concrete surface markedly changed during wetting-drying cycles relative
to the inner core, which led to further deformations. Figure 5.10 shows the change in crack width
for slab G-WD which was subjected to 5 wetting-drying cycles over 112 days. In the last cycle
(22 °C with 100% RH and 35 °C with 30% RH) the crack width varied between 0.23 and 0.46
mm. The lower crack width recorded during the wetting periods can be attributed to swelling of
the slab due to the increase in relative humidity, which led to partial closure of the crack
opening. Subsequently, excessive drying of the slab increased the crack width up to 0.46 mm (in
the last cycle), which is 0.92% and 0.39% higher than that crack width measured before the
wetting and drying exposure and in the normal exposure (slab SG3 after exposure for 112 days),
respectively.
Chapter5: Results and Discussion-environmental Conditions
102
62Fig. 5.6: Development of the bar strains in the slab G-FT under freeze-thaw conditions.
63Fig. 5.7: Development of the bar strains in the slab G-FT under freeze-thaw conditions during
the last cycles.
0
500
1000
1500
2000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
500
1000
1500
2000
-25 -20 -15 -10 -5 0 5 10
Str
ain
(μ
ɛ)
Temprature (°C)
Last cycle (163)-G-FT
Chapter5: Results and Discussion-environmental Conditions
103
64Fig. 5.8: Concrete surface appearance in different environmental conditions: (a) wet-dry, (b)
normal, and (c) freeze-thaw, and (d) Surface scaling mechanism.
65Fig. 5.9: Surface scaling.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Wei
gh
t lo
ss
(Kg
/m2
)
Time(days)
G-FT G-WD
Chapter5: Results and Discussion-environmental Conditions
104
66Fig. 5.10: Crack width development in the slab G-WD under wet-dry conditions.
Corresponding to the crack width trend, the strain in the GFRP bars increased from 1400 με
(wetting portion) to 2250 με (drying portion) in the last cycle (Fig. 5.11), due to the additional
drying shrinkage deformation under hot-arid conditions, which was restrained by the GFRP
reinforcement. It should be noted that this value is significantly higher than the maximum strains
recorded in the normal (1520 με) and freezing-thawing (1690 με) exposures. This behavior was
confirmatory to the measurements of concrete surface strain that increased up to 480 με due to
the additional shrinkage during the drying portion (Fig. 5.12).
5.5 MATERIALS TESTS
In additional to the early-age cracking of restrained concrete slabs exposed to harsh conditions,
they were vulnerable to material degradation especially at the mid-length (in the vicinity of the
crack) due to temperature and humidity variations. To capture this trend, three materials tests
Dynamic Modulus of Elasticity (DME), Rapid Chloride Permeability Test (RCPT), and
0
0.1
0.2
0.3
0.4
0.5
0.6
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Cra
ck W
idth
(m
m)
Time (days)
Permissible crack width for FRP-RC structures according to CHBDC
Chapter5: Results and Discussion-environmental Conditions
105
Scanning Electron Microscopy (SEM) were conducted on eight cores (close and away from left
and right sides of the crack) extracted from slabs G-WD and G-FT; four cores each.
5.5.1 UPV Test (Ultrasonic Pulse Velocity Test)
Table 5.1 shows the dynamic modulus of elasticity results for the concrete used before
(unexposed specimens) and after (cores) being subjected to freezing-thawing and wetting-drying
conditions. While the test results were in the narrow range of 45-50 GPa, they showed a general
reduction (maximum of 10%) of DME for the concrete exposed to cyclic conditions, which
indicates the existence of fissures and micro-cracks in the cementitious matrix.
5.5.2 RCPT Test (Rapid Chloride Permeability Test)
After and before being subjected to different environmental conditions, top 50-mm think slices
were cut from all 100 mm diameter cylindrical cores. After operating the RCPT for 6 hours
according to ASTM C1202 (Standard Test Method for Electrical Indication of Concrete’s Ability
to Resist Chloride Ion Penetration), the penetration depth was measured on concrete specimens
extracted from different locations in the slabs subjected to freezing-thawing and wetting-drying
conditions. The whitish color of the penetration depth was clearly visible as depicted in Fig.
5.13, and the results are listed in Table 5.1. In contrast to the freezing-thawing exposure, Table
5.1 shows that the specimens extracted from the slab subjected to wetting-drying cycles yielded
relatively higher penetration depths in the vicinity of the crack location, which signifies that the
pore structure was highly interconnected in these specimens. This can be attributed to a higher
intensity of micro-cracks due to the matrix fatigue resulting from high strain fluctuations of
repetitive swelling and shrinkage in the wetting-drying exposure. These results are consistent
with the higher concrete and reinforcement strain values for the spacemen G-WD exposure to
drying conditions.
Chapter5: Results and Discussion-environmental Conditions
106
67Fig. 5.11: Development of the bar strains in the slab G-WD under wet-dry conditions.
68Fig. 5.12: Surface strain of the concrete in the vicinity of the first crack.
0
500
1000
1500
2000
2500
3000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
-600
-500
-400
-300
-200
-100
0
100
200
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
Chapter5: Results and Discussion-environmental Conditions
107
69Fig. 5.13: Chloride penetration depth in cores extracted from: (a) slab G-FT close to the crack
area, (b) slab G-FT out of the crack area, (c) slab G-WD close to the crack area (d) slab G-WD
out of the crack area.
11Table 5.1: DME and RCPT results
Exposure Cores
Dynamic Modulus of Elasticity
(GPa)
Average Penetration Depth
(mm)
Normal
(un-exposed)
C-R 50 7
C-L 49 6
A-R 52 5
A-L 51 6
Freezing and
Thawing
C-R 48 8
C-L 49 8
A-R 46 7
A-L 48 8
Wetting and
Drying
C-R 48 9
C-L 48 12
A-R 47 8
A-L 45 8
C: Center, A: Away from center, L: Left, R: Right
Chapter5: Results and Discussion-environmental Conditions
108
5.5.3 Microstructural Analysis
To supplement the results of UPV and RCPT, the alteration of microstructure of concrete was
also assessed by backscattered scanning electron microscopy (BSEM) on thin sections from
cores extracted from G-FT and G-WD in the vicinity and away from the main crack. The
polished sections were prepared from fracture surfaces that were dried at 40 °C for 24 h,
impregnated with low-viscosity epoxy resin under pressure, cut, polished and carbon coated.
The SEM micrographs show that the specimen subjected to wetting-drying conditions
particularly in the vicinity of the main crack (Fig. 5.14 (a)) had higher intensity of micro-cracks
and internal damage than that of the concrete exposed to freezing-thawing cycles (Fig. 5.14 (b)).
This trend is consistent with the RCPT test, the higher recorded concrete and reinforcement
strain values in the vicinity of the crack, and the crack width for the specimen under wetting-
drying conditions.
70Fig. 5.14: Typical SEM micrographs from: (a) specimen G-WD (slab under wetting and drying
conditions), and (b) specimen G-FT (slab under freezing and thawing conditions) at vicinity of
the main crack.
Chapter 6: Numerical Analysis
109
CHAPTER 6: NUMERICAL ANALYSIS
6.1 GENERAL
Generally, the verification and revision of any design provisions or guidelines require a
reasonable population of data with a wide range of variables. However, the research in the area
of FRP-RC structures is still very limited possibly due to the inherent difficulties in simulating
restrained shrinkage in full-scale specimens in the laboratory. Therefore, the early-age behavior
of GFRP-RC bridge deck slabs subjected to shrinkage is still largely unexplored. The Finite
Element Modeling (FEM) provides an effective tool to simulate laboratory conditions with a
high degree of accuracy for any complex structural experiment without the constraints of time
and cost. This numerical study aims to investigate the effect of key design parameters, namely,
concrete strength and cover as well as reinforcement type and spacing, on early-age cracking of
FRP-RC bridge deck slabs.
In this chapter a finite element model (FEM) for predicting early-age behavior of reinforced
concrete (RC) bridge deck slabs with fiber-reinforced polymer (FRP) bars is presented. The FEM
was constructed using specialized software for the analysis of RC structures: ATENA (Version
5). The results of the model were verified against the phase I experimental test results of four
full-scale end-restrained slabs (2500 mm long × 765 mm wide × 180 mm thick). The model was
verified for cracking pattern, crack width and spacing, and reinforcement strains in the vicinity of
the crack using different types and ratios of longitudinal reinforcement. The FEM was able to
predict the experimental results within 6 to 10% error. The verified FEM was utilized to conduct
a parametric study investigating the effect of five key parameters including reinforcement
surface texture, bar spacing, concrete cover, FRP bar type, and concrete compressive strength on
the behavior of FRP-RC bridge deck slabs subjected to restrained shrinkage at early-age.
Chapter 6: Numerical Analysis
110
6.2 NUMERICAL STUDIES
A limited number of parametric studies using FEM have been carried out on steel-RC bridge
deck slabs subjected to shrinkage. According to a FEM study conducted by Hadidi and
Saadeghvaziri (2005), it was concluded that slab sectional stiffness and girder spacing have a
significant impact on early-age cracking patterns and stress histories in steel-RC bridge deck
slabs. Also, Munnetyan et al. (2011) performed a non-linear FEM (using ABAQUS software) to
examine the effect of temperature variation in the external steel girders on early-age cracking in
RC bridge deck slabs. They found that cooling the lower flange of the girder, at negative moment
regions, during concrete hydration would increase the compressive stresses at the surface of the
deck after dissipation of the hydration heat and mitigate tensile stresses due to drying shrinkage.
6.3 FINITE ELEMENT MODEL (FEM)
This section introduces the fundamental steps to construct the FEM including element types,
material models and boundary conditions. A total of four element types were defined in this
program to model concrete, steel support plates, end steel bars and main FRP reinforcement.
In the experimental study all slabs were effectively anchored at its ends by 1473×1000×1200
mm concrete blocks. However, in the FEM, those blocks were replaced with 50-mm thick stiff
steel end plates to reduce number of elements and solution time. The model generated is shown
in Fig. 6.1 (a and b). One-dimensional (1-D) reinforcement bars were added to the model by first
creating two joints to define the start and end points of the reinforcement. The reinforcement
layout of the model is shown in Fig. 6.1(c).
Chapter 6: Numerical Analysis
111
71Fig. 6.1: Model geometry: (a) side view (b) 3D view of the analytical model based on the
experimental test specimens, and (c) locations of the reinforcing bars (all dimensions are in mm).
6.3.1 Concrete
The 3-D eight-node solid brick element (Fig. 6.2) was used to model the geometry of the slabs
(except the corner parts). A brick element is only available to be used for hexahedron-shaped
elements. This element is defined by 8 corner nodes with five degrees of freedom (DOFs) at each
node (Cervenka et al. 2012), as well as 12 additional integration points as shown in Fig. 6.2 (b).
The brick element is ideal to use whenever it can be since it is generally accurate and can
significantly reduce analysis time required by the computer compared to the other element types
Chapter 6: Numerical Analysis
112
(Cervenka et al. 2005). The geometry of the corner parts were modeled using 3-D four-node
tetrahedron solid elements. This element is defined by 4 corner nodes with five DOFs at each
node (Cervenka et al. 2012), as well as with 6 additional integration points as shown in Fig
6.2(c). Tetrahedron element should be used whenever there is some sort of irregularity in an
element, such as an opening on its surface or triangle-shaped elements. The tetrahedron element
is more flexible than a brick element but can also result in increased processing time (Cervenka
et al. 2005).
72Fig. 6.2 Different finite element types used: (a) top view of the finite element mesh of the
analytical model (b) brick element, and (c) tetrahedron element.
Chapter 6: Numerical Analysis
113
In this study, the material model “CC3DNonLinCementitious2Variable” was assigned for both
concrete brick and tetrahedron elements. Since the concrete properties changes versus time, this
material model allows to define time-dependent properties for concrete. Therefore, the equation
recommended by ACI 209.2R-08 (ACI 2008), Eq. 6.1, was adopted to estimate the strength
development of concrete as a function of time, using concrete compressive strength at age 28
days (t (day) and 𝑓′𝑐,𝑡, 𝑓′𝑐28 (MPa)).
𝑓′𝑐,𝑡 = [𝑡
4+0.85𝑡] 𝑓′𝑐28 [Eq. 6.1]
The “CC3DNonLinCementitious2Variable” material model is able to account for the
nonlinearity of concrete and provides smeared cracking information in the three main
perpendicular directions. The concrete fracture is modelled by a smeared crack model based on
Rankine tensile criterion (Cervenka et al. 2012). The concrete plasticity model is based on the
Menetrey-William failure surface equation (Cervenka et al. 2012). The Menetrey-Willam failure
surface adopts the uniaxial compressive test of concrete based on the experimental work of Van
Mier (Cervenka et al. 2012), where in the concrete stress-strain relationship, the softening curve
is linear (Fig. 6.3). The elliptical ascending part is given by the following equations:
𝜎 = 𝑓′𝑐𝑜+ (𝑓′
𝑐− 𝑓′
𝑐𝑜)√1 − (
𝜀𝑐− (𝑓′𝑐 /𝐸𝑐)
𝜀𝑐)2 [Eq. 6.2]
Where 𝑓′𝑐𝑜
=2𝑓′𝑡 [Eq. 6.3]
𝑊𝑑 = (𝑓′𝑐 /𝐸𝑐 − 𝜀𝑐
𝑝)𝐿𝑐 [Eq. 6.4]
where 𝜎 is the concrete compressive stress (MPa), Ec is the concrete modulus of elasticity (GPa),
𝑓′𝑐 and 𝑓′
𝑡 are the concrete compressive and tensile strength (MPa), respectively, Wd is the end
point of the softening curve (Wd = - 0.0005 mm for normal strength concrete as recommended by
Chapter 6: Numerical Analysis
114
the software guidelines), 𝑓𝑐𝑜 is the starting point of the non-linear curve (MPa), 𝜀𝑐𝑝
is the value of
plastic strain at the max compressive strength, on the descending curve, and Lc is the element
length scale parameter.
The cracking behavior of concrete was modeled according to the equation developed by
Hillerborg et al. (1976) (Eq. 6.5) as represented in Fig. 6.3 (c). The width of crack in this
equation is calculated based on three factors: the shape of the softening curve, tensile strength
and fracture energy. The effect of tension stiffening where cracks cannot fully develop along the
section is also considered. Tension stiffening is simulated by specifying a factor that represents
the relative limiting value of tensile contribution as a fraction of the tensile capacity of the
concrete.
𝜎
𝑓𝑡′ =
(
1 + 3067
𝑤5.14Gf
𝑓𝑡′
⁄
)
3
𝑒𝑥𝑝(−6.93𝑤
5.14𝐺𝑓𝑓𝑡′⁄) −
𝑤5.14𝐺𝑓
𝑓𝑡′
⁄(1 + 30673) [Eq. 6.5]
where w is the crack width (mm), Gf is the concrete fracture energy (MN/m), 𝜎 is concrete actual
tensile stress (MPa), and 𝑓′𝑡 is the concrete tensile strength (MPa). The software generates the
concrete properties using the concrete cube strength, 𝑓′𝑐𝑢 (MPa). Equation 6.5 was used to define
concrete cube strength from standard cylinders tests. Poisson’s ratio was assumed to be 0.2, and
the concrete tensile strength, 𝑓′𝑡 (MPa), initial modulus of elasticity (Ec) (MPa), and fracture
energy (Gf) (MN/m) were calculated based on the following equations used in this software
(Cervenka et al. 2012):
𝑓′cu = 1.15 𝑓′c [Eq. 6.6]
𝑓′𝑡 = 0.24 (𝑓′𝑐𝑢) 2/3
[Eq. 6.7]
Chapter 6: Numerical Analysis
115
Ec = (6000 - 15.5 𝑓′c) √𝑓′𝑐𝑢 [Eq. 6.8]
Gf = 0.000025 𝑓′t [Eq. 6.9]
73Fig. 6.3: Van Mier compressive stress-strain relationship of the concrete: (a) non-linear
ascending part (b) linear descending (softening) part, and (c) stress-crack opening according to
Hodjik law (reproduced from Cervenka et al. 2012).
6.3.2 Steel Support Plates
Lines along the surfaces of the outside edges of the end steel plates were fixed in all directions to
simulate fixed end conditions. These plates were modeled using the same brick element but with
the 3-D Elastic Isotropic material. The yield strength, modulus of elasticity, and Poisson’s ratio
were assumed to be 420 MPa, 200 GPa and 0.3, respectively.
6.3.3 Reinforcing Bars
Since the bar spacing is an important factor affecting the cracking behavior, the discrete method
was selected for modeling reinforcement in the concrete. In this regard, the 1-D “Reinforcement”
Chapter 6: Numerical Analysis
116
truss element was used for both FRP and steel reinforcing bars. The basic characteristics of the
steel reinforcement were determined using a bi-linear form with yield strength and elastic
modulus of 420 MPa and 200 GPa, respectively. The GFRP reinforcement has a linear elastic
behavior up to failure. Table 6.1 provides the material properties of the reinforcement used in the
FEM.
12Table 6.1: Mechanical properties of GFRP, CFRP and steel bars
Bar type Bar diameter
(mm)
Bar area
(mm2)
Modulus of
elasticity
(GPa)
Tensile strength
(MPa)
Tensile
strain
(%)
GFRP #4 12.7 127 65 1453 2.23
GFRP #5 15.9 198 62 1450 2.23
GFRP #6 19.1 285 63 1484 2.35
CFRP #4 12.7 127 144 1899 1.32
CFRP #5 15.9 198 140 1648 1.18
Steel 15M 16 200 200 *fy = 420
*ɛy = 0.21
Steel 25 M 25 500 200 fy = 420 ɛy = 0.21
*fy: Steel yield strength, ɛy: Steel yield strain.
The bond stress-slippage relationship between concrete and reinforcement has a significant effect
on the performance of RC structures. For this model, the stress-slippage relationship was defined
using the “Bond for Reinforcement” option. Different bond stress-slippage relationships were
used to define the response of bond elements for the steel, GFRP and CFRP bars. The stress-
slippage model recommended by CEB-FIP Model Code (CEB-FIP 1990) was used for steel bars
(Fig. 6.4). The interface between reinforcement and surrounding concrete used for different
surface pattern of CFRP bars were based on the study by Mavar et al. 2003 (Fig. 6.4). For sand-
Chapter 6: Numerical Analysis
117
coated and ribbed-deformed GFRP bars, the interfaces were defined based on the study by Alves
et al. 2011 and manufacture specifications, respectively (Fig. 6.4).
74Fig. 6.4: Bond-slip relationship for different types of reinforcement in concrete at 3 days.
6.3.4 Meshing of the Model
In this study, each specimen was meshed into 8545 finite elements with a side length of 50 mm
each. Also, each steel end-plate was meshed into 124 elements. Since the program automatically
generates embedded finite elements for the reinforcement bars, 1-D entities such as bar does not
need to be meshed by the user before the model analysis is started.
6.3.5 Shrinkage Profile
To estimate the shrinkage profile of concrete, ACI 209.2R-08 (ACI 2008) recommends different
models such as ACI 209 (Eq. 6.10), Bažant-Baweja B3 (Eq. 6.11), GL2000 (Eq. 6.12) and CEB-
FIP/90 (Eq. 6.13) to predict time-dependent shrinkage of concrete.
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Bo
nd
str
ess
(MP
a)
Slip (mm)
Steel GFRP-SC GFRP-RD CFRP-SC CFRP-RD
Chapter 6: Numerical Analysis
118
𝜀𝑠ℎ(𝑡)(𝐴𝐶𝐼 209) = (𝑡−𝑡𝑐)
26𝑒{𝑣𝑠⁄ 1.42×10
−2}+(𝑡−𝑡𝑐)𝛾𝑠ℎ(−780) × 10
−6 [Eq. 6.10]
𝜀𝑠ℎ(𝑡)(𝐵3) = 𝑡𝑎𝑛ℎ√(𝑡−𝑡𝑐)
0.85𝑡𝑐−0.08𝑓𝑐𝑚28
−0.25[2(𝑣 𝑠⁄ )]2 𝑘(ℎ) ×– 𝜀𝑠ℎ∞ [Eq. 6.11]
𝜀𝑠ℎ(𝑡)(𝐺𝐿2000) = [(𝑡 − 𝑡𝑐)
{𝑡 − 𝑡𝑐 + 0.12(𝑣𝑠⁄ )2}⁄ ]0.5𝛽(ℎ) ×– 𝜀𝑠ℎ𝑢 [Eq. 6.12]
𝜀𝑠ℎ(𝑡)(𝐶𝐸𝐵−𝑀𝐶90) = [(𝑡−𝑡𝑐)
350[(𝑣 𝑠⁄ )
50⁄ ]
2
+(𝑡−𝑡𝑐)
]0.5 𝛽𝑅𝐻(ℎ) × 𝜀𝑐𝑠𝑜 [Eq. 6.13]
Where γsh represents the cumulative product of the applicable correction factors for fresh
concrete properties and ambient humidity conditions in the ACI 209 model, εsh∞, εshu and εcso are
the notional ultimate shrinkage (mm/mm) based on RILEM data bank (RILEM 1998) for
Bazant, GL 2000 and CEB-MC90 equations, respectively. Also, K(h), β(h), and βRH(h) are the
ambient relative humidity factor for Bazant, GL2000 and CEB-MC90 models. Moreover, t and tc
are the concrete age and curing time (day), respectively, and v/s is member’s volume-to-surface
ratio (mm). In these models the concrete was assumed to be moist cured at least for 1-14 days.
It is well-documented in the literature (Mehta and Monteiro 2014; Sakata and Ayano 2001) that
ambient environmental conditions in terms of combined temperature and humidity changes
affect the amount of concrete shrinkage. However, the effect of temperature on concrete
shrinkage is explicit in most of the prediction equations mentioned above. Nevertheless, the
CEB-MC90 model incorporates the effect of temperature as well as humidity to predict the
shrinkage of concrete versus time. When a constant temperature above 30 ºC is applied while the
concrete is drying, CEB MC90 recommends Eq. 6.14 to predict concrete shrinkage.
Chapter 6: Numerical Analysis
119
𝜀𝑠ℎ(𝑡,𝑇)(𝐶𝐸𝐵−𝑀𝐶90) = [𝑡−𝑡𝑐
350[𝑣𝑠⁄
50]2
exp[−0.06(𝑇−20)]+(𝑡−𝑡𝑐)
]
0.5
× 𝛽𝑅𝐻(ℎ) [1 + (0.08
1.03−ℎ) (
𝑇−20
40)] × 𝜀𝑐𝑠𝑜 [Eq. 6.14]
where h and T are the ambient relative humidity (%) and temperature (ºC), respectively.
In the experimental study, all prototypes were kept inside a plastic tent for 1 day after casting.
The profile of shrinkage was accelerated at early-age by increasing the temperature in the tent to
35 °C in the first day followed by exposing the slabs to air flow of 50 km/h for 6 days. Table 6.2
provides the environmental conditions applied to all specimens. The CEB-MC90 model was
modified to account for the temperature and humidity changes shown in Table 6.2.
13Table 6.2: Environmental conditions applied to the slabs versus the time of exposure
Time
(day)
Temperature
(ºC)
Humidity
(%) Ambient conditions
1 35 85 Slabs subjected to a hot temperature inside a
tent
2-7 22 40 Slabs subjected to air flow by fans
8-112 22 65 Slabs subjected to laboratory conditions
The shrinkage strain of concrete εTotal subjected to different environmental conditions was
calculated using Eq. 6.15:
𝜀 𝑇𝑜𝑡𝑎𝑙 = 𝜀𝑠ℎ(𝑡)(𝐶𝐸𝐵−𝑀𝐶90) + 𝛼3𝛥𝑇 + 𝐴𝐹 [Eq. 6.15]
where: α3 is the concrete coefficient of thermal expansion at age of 3 days (~2.55×10-6
per ºC,
obtained by ASTM-E831 2013), ΔT is temperature change (ºC) between incremental time steps
and AF is the effect of air flow on concrete shrinkage (με).
Table 6.3 shows the concrete free shrinkage versus that predicted by the modified CEB-MC90
model (Eq.15). Test results indicate that the advent of air flow at 2 to 7 days led to steady-state
Chapter 6: Numerical Analysis
120
shrinkage. Therefore, the rate of shrinkage in this time interval can be calculated by linear
interpolation at a rate of 18.2 με/day. The main part of drying shrinkage caused by air flow (AF)
occurred within 2-7 days, therefore the remaining shrinkage predicted by CEB-MC90 was
distributed within 8-112 days using the model’s time function (Eq. 6.16).
Figure 6.5 indicates that the modified CEB-MC90 model could reasonably predict the concrete
total shrinkage based on the applied environmental conditions.
CEB-MC90 time function= [(𝑡−𝑡𝑐)
350[(𝑣 𝑠⁄ )
50⁄ ]
2
+(𝑡−𝑡𝑐)
]
0.5
[Eq. 6.16]
In addition, for high-strength concrete, CEB MC90 model has been developed (CEB 1999) to
take into account the particular characteristics of concrete strength. The modified CEB-MC90/99
model subdivides the total shrinkage into the components of drying and autogenous shrinkage
(Eq. 6.17). Therefore, in the parametric study, this model was used to predict concrete shrinkage
for different concrete strength.
εsh(t,tc) = εcaso(fcm28)βas(t) + εcdso(fcm28)βRH(h)βds(t) [Eq. 6.17]
where: fcm28 represents concrete mean compressive strength (fcm28(ACI 318-11a)=1.1f’c+5) (MPa), f’c
is the concrete compressive strength (MPa), εcaso(fcm28) is the nominal autogenous shrinkage
coefficient, and βas(t) is the function describing the time development of autogenous shrinkage,
εcdso( fcm28) is the nominal drying shrinkage coefficient, βRH(h) is the ambient relative humidity for
drying shrinkage, and βds(t) is the function describing the time development of drying shrinkage.
Chapter 6: Numerical Analysis
121
14Table 6.3: The predicted and experimental values of free shrinkage
Time
(day)
Predicted
shrinkage
per each
day by
CEB-
MC90
(με)
α3ΔT
(με)
Total
Shrinka
ge rate
due to
air flow
(με)
Shrinka
ge due
to
AF
(με)
Predicted
shrinkage
per each
day by
modified
CEB-
MC90 (με)
Cumulative
predicted
shrinkage
by
modified
CEB-
MC90 (με)
Cumulative
predicted
shrinkage
by CEB-
MC90 (με)
Cumulativ
e
experimen
tal
shrinkage
value (με)
1 -18.000 -33.000 0.000 0.000 -51.000 -51.000 -18.000 -60.000
2 -11.615
0
-18.160 -6.545 -18.160 -69.160 -29.615 -95.000
3 -6.629 -18.160 -11.531 -18.160 -87.320 -36.244 -113.000
4 -5.576 -18.160 -12.584 -18.160 -105.480 -41.819 -132.000
5 -4.901 -18.160 -13.259 -18.160 -123.640 -46.720 -155.000
6 -4.421 -18.160 -13.739 -18.160 -141.800 -51.141 -167.000
7 -4.056 -18.160 -14.104 -18.160 -159.960 -55.198 -169.000
28 -0.130
0 0
-0.130 -167.451 -74.992 -169.447
42 -0.103 -0.103 -169.045 -90.931 -169.745
56 -0.086 -0.086 -170.349 -103.971 -170.043
70 -0.075 -0.075 -171.465 -115.128 -170.340
90 -0.063 -0.063 -172.832 -128.799 -170.766
112 -0.054 -0.054 -174.115 -141.629 -171.000
6.3.6 Analysis
The geometric and material non-linear solution was taken into account by the program using the
concept of incremental step-by-step analysis. The shrinkage was applied in 112 load increments;
each represents one day of the shrinkage load. At each increment, load iterations were performed
until the convergence criteria were satisfied. Four solution errors serve to check convergence
criteria: displacement increment normalized residual force, absolute residual force, and energy
dissipated (Cervenka et al. 2012). After reaching the equilibrium and completion of each loading
Chapter 6: Numerical Analysis
122
step, the stiffness matrix was adjusted to reflect the non-linear changes before proceeding to the
next load step. In this regard, the program adopts full Newton-Raphson method to modify the
solution parameter. It should be noted that the solving time for running each model was
approximately 50 hours.
75Fig. 6.5: Experimental and predicted shrinkage values.
6.3.7 Model Verification
For the verification process, the experimental results of the four bridge deck slabs were used.
The constructed model was calibrated against specimen SG2 and then tested on the remaining
specimens to ensure that the results remained within a reasonable error. The model was verified
in terms of crack width, crack pattern and average tensile strains in the reinforcement at the crack
location. For generalization of the FEM, the predicted shrinkage by modified CEB-MC90
method, assuming wet curing conditions, was also applied to the model. The FEM results for
-200
-150
-100
-50
0
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time (days)
Exp. Modified CEB-MC90 CEB-MC90
Chapter 6: Numerical Analysis
123
crack width and reinforcement strain remained within a reasonable error of 6% and 10%,
respectively. Also, the main crack pattern in the FEM was recorded at a similar location to the
experimental program; however, the secondary cracks did not occur in the FEM which were
contradicted with the experimental study for specimens SG4 and SS.
6.3.7.1 Cracking pattern
Figure 6.6 shows the cracking pattern for the FEM models and experimental tested slabs. In the
experimental study, there was one main crack located at the middle reduced cross section of the
slab. The main cracking pattern for the FEM models accurately predicted the crack pattern
observed in the experimental program at the middle section. The experimental results indicate
that an increase in the reinforcement area or modulus of elasticity (SG4 and SS compared to SG2
and SG3) leads to less stiffness reduction at first cracking (mid-span), thus the restraining force
after cracking remains high. With such high restraining force, the development of additional
drying shrinkage or temperature variation causes the concrete in regions away from the first
crack to experience further cracking. However, the FE results did not record secondary crack
pattern on the models for SG4 and SS.
6.3.7.2 Crack width
In the FEM, the crack width was considered as the average of the displacements measured by
monitoring points at two locations across the slab width at mid-span (replicating the same
approach as that of the PI gauges used in the experimental study). Figure 6.7 represents the crack
width development curves for the experimental and the numerical study. The crack width-time
diagrams show several important relationships for the models. In the finite element model for
SG2 (ρ = 0.5%), the crack width reached the allowable value of 0.5 mm (ACI 440 2006, CSA
2006) after 5 days. After 112 days, this crack width reached 0.67 mm. The FEM results reveal
Chapter 6: Numerical Analysis
124
that for SG3 (ρ = 0.7%), SG4 (ρ = 1.1%) and SS (ρ = 0.7%), the crack width were 0.34, 0.26 and
0.20 mm after 112 days. The predicted crack widths in the FEM lie within an average error of
6%. The comparison between the results shows that the FEM was able to accurately predict the
final crack width for the GFRP and steel RC slabs (Fig. 6.7).
76Fig. 6.6: Concrete stresses in the Y direction (MPa) and cracking pattern.
Chapter 6: Numerical Analysis
125
77Fig. 6.7: Experimental and FEM results for the development of crack width with time for slabs
SG2, SG3, SG4 and SS.
6.3.7.3 Reinforcement strain
In the experimental study, the strains in main reinforcement were measured by strain gauges
attached to each rebar at mid-span. A similar approach was followed in the FEM by defining
four monitoring points at the same locations. Figure 6.8 shows the predicted and experimental
tensile strains in reinforcement at the cracking location. The results show that, once a crack
developed at mid-span, the average strain in reinforcement increased rapidly. This value
decreased with increasing the reinforcement ratio or modulus of elasticity. In FEM for SG2,
SG3, SG4 and SS, the average strains in the bars at crack location were 2590, 1400, 1130 and
480 με after 112 days. However, the strain away from cracking location was still less than 200
με. The strain in the reinforcement at the crack location was also efficiently predicted by FEM
subjected to shrinkage within an average error of 10% (Fig. 6.8).
Chapter 6: Numerical Analysis
126
78Fig. 6.8: Experimental and FEM results for the development of bar strains at crack location for
slabs SG1, SG2, SG3 and SS.
6.3.7.4 Model verification for slabs subjected to freeze-thaw and wet-dry cycles
The cyclic wet-dry and freeze-thaw are described as the main ambient conditions which may
lead to volume instability in the restrained concrete deck slabs. Volume changes due to repetitive
shrinkage/swelling may lead to material fatigue and de-bonding of reinforcement (Zhang et al.
2012; Ayano et al. 2002). Therefore, these conditions can be considered critical in the durability-
based design of concrete structures.
It is well-known that the most of the materials except water experience expansion and
contraction when they are exposed to hot and cold environments, respectively. Water molecule is
composed of two hydrogen atoms connected with an oxygen atom. Their connection angel in the
liquid state is 105° 06’, when water changes into the ice state, the connection angel increases to
Chapter 6: Numerical Analysis
127
109° 28’ (Krylov 1997). This phenomenon increases the volume of the water by about 9%.
Therefore in the concrete with high internal relative humidity (RH>90%) water plays an
important role on the concrete volumetric instability when it is subjected to freeze/thaw
conditions.
According to the experimental results for the specimen subjected to freeze-thaw conditions,
crack width and bar strain at the vicinity of the main crack reached to their maximum and
minimum point at +4 °C (thawing) and -18 °C (freezing), respectively, in each cycle. This
behaviour is attributed to the frost action in the saturated concrete. The effect of frost action on
the concrete was studied by many researchers (Towers and Helmuth 2008; Scherer et al. 2002;
Krylov 1997). It is found that, at the onset of ice crystallization in the saturated concrete, the
frictional resistance to ice growth creates internal pressure in the pores leading to concrete
expansion. However, the crack width and bar strain in the vicinity of crack location in the FEM
for G-FT were 0.38 and 0.31 mm, and 1460 and 1440 με corresponding to the freezing and
thawing stages, respectively (Figs. 6.9 and 6.10).
Experimental results for the specimen subjected to wet-dry conditions indicate that the higher
crack width and bars strain in the vicinity of the main crack were recorded during the drying
periods, this behaviour can be attributed to the accelerated drying shrinkage due to high ambient
temperature (35 ºC), which led to partial opening of the crack. While the FEM for the G-WD
shows expansion in the model due to increasing ambient temperature to 35 ºC (Figs. 6.11 and
6.12).
Chapter 6: Numerical Analysis
128
79Fig. 6.9: Crack width development in the slab G-FT under freeze-thaw conditions during first
cycle.
80Fig. 6.10: Development of the bar strains in the slab G-FT under freeze-thaw conditions during
first.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-25 -20 -15 -10 -5 0 5 10
Cra
ck w
idth
(mm
)
Temperature (ºC) FEM Exp.
0
500
1000
1500
2000
2500
3000
-25 -20 -15 -10 -5 0 5 10
Str
ain
(μ
ɛ)
Temperature (ºC) FEM Exp.
Chapter 6: Numerical Analysis
129
81Fig. 6.11: Crack width development in the slab G-WD under wet-dry conditions.
82Fig. 6.12: Development of the bar strains in the slab G-WD under wet-dry conditions.
Finite element analytical results appear to contradict those results were obtained in experimental
study for the specimens subjected to freeze-thaw and wet-dry conditions. This can be explained
by the fact that software is not capable to consider the effect of internal water when the concrete
is exposed to freezing or drying conditions.
6.3.8 Parametric Study
This study examined the effect of concrete compressive strength, concrete cover, reinforcement
type, and bar spacing on the early-age behavior of FRP-RC bridge deck slabs subjected to
shrinkage. Since the FEM results for SG3 were the closest to those of the experimental results, the
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 14 28 42 56 70 84 98 112
Cra
ck W
idth
(m
m)
Time (days) FEM Exp.
0
1000
2000
3000
0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
Str
ain
(μ
ɛ)
Time(days)
Exp. FEM
Chapter 6: Numerical Analysis
130
parametric study models were developed based on the same assumptions and geometry that were
used for modeling slab SG3 in the verification stage. Moreover, the reinforcement ratio for this slab
(0.7%) is recommended as the minimum reinforcement ratio for GFRP-RC bridge deck slabs by
CHBDC (2006). Table 6.4 provides details of the parametric FEM. The results are presented in
terms of cracking pattern and crack width development and reinforcement strain.
6.3.8.1 Concrete compressive strength
In this study, six concrete compressive strengths 30, 40, 50, 60, 70 and 80 MPa were used in the
FEM. The applied concrete shrinkage load scheme was obtained according to the CEB MC90-99
method, meeting the requirements of a 3-day moist curing conditions (ACI 209 2008). The
predicted shrinkage values indicate that increasing the strength from 30 to 80 MPa intensifies the
autogenous shrinkage and consequently increases the concrete total shrinkage value from 170 to
230 μɛ (Table 6.5).
Figure 6.13 (a) shows the typical cracking pattern for different concrete strengths at the notched
mid-span location, while Figure 6.13 (b) illustrates the change in crack width and reinforcement
strain over 112 days. As concrete strength was increased from 30 to 80 MPa, the crack width and
associated reinforcement strain at crack location grew from 0.33 to 0.48 mm and from 1400 to
2020 με, respectively. It is well-documented (Mehta and Montherio 2014) that, in high-strength
concrete (with low water-to-binder ratio), consuming water content during the hydration process
intensifies autogenous shrinkage in comparison to normal strength concrete. This self-
desiccation effect was considered in the predicted load scheme by CEB-MC 90/99, as shown in
Table 6.5. Furthermore, bridge deck slabs with high strength concrete offer greater sectional
stiffness, which increased the internal restraint, and thus led to an increase in restrained force.
Chapter 6: Numerical Analysis
131
6.3.8.2 Reinforcing bar spacing
In this study, the effect of reinforcement bar spacing on crack control was investigated. A
constant reinforcement ratio of ρ = 0.70% was distributed to 2, 3, 4, 5, 6 and 7 bars (top and
bottom) which dictates the spacing ranged between 96 and 255 mm. Figure 6.14 (a) shows the
typical cracking pattern for the FEM with different bar spacing at the notched mid-span location.
In these models, the cracks typically occurred at mid-span. Results show that reducing the bar
spacing from 255 to 96 mm decreases the early-age crack width from 0.34 to 0.29 mm and
increases the average value of reinforcement strain from 1400 to 1880 με, respectively (Fig. 6.14
(b)). These results are in good agreement with previous findings (Frosch et al. 2006) which
indicate reducing the bar spacing increases the contribution of the reinforcement on early-age
crack-width control in bridge deck slabs subjected to shrinkage.
6.3.8.3 Concrete cover
The effect of increasing the concrete cover from 5 to 85 mm on crack control was investigated.
Figure 6.15 (a) shows the typical crack pattern occurred at mid-span for all models with different
thickness of concrete cover. The results in Fig. 6.15 (b) indicate that, for the GFRP-RC members
subjected to axial tension (shrinkage) with different concrete covers, the crack width and the
average strain on the bar at crack location remain constant within 0.34~0.35 mm and 1320~1330
με, respectively. The full-depth cracks develop under axial tension (shrinkage) are parallel-sided,
which is different from flexural cracks. Therefore, the crack width and strain on the bar at crack
location are less dependent on the amount of concrete cover.
6.3.8.4 Reinforcement type
Different types of GFRP and Carbon FRP (CFRP) (sand-coated and ribbed-deformed) can be
used as internal reinforcement in bridge deck slabs. The magnitude of crack width depends on
Chapter 6: Numerical Analysis
132
several factors related to reinforcement type such as quality of bond between concrete and
reinforcing bars and modulus of elasticity of reinforcement material. In this study, the effect of
reinforcing bar type on crack control was investigated using the constructed FEM with a constant
reinforcement ratio of ρ = 0.70%. These models had two different FRP types (CFRP and GFRP)
with two different bar surface textures (sand-coated and ribbed-deformed). In addition, since the
modulus of elasticity of CFRP bars is higher than that of GFRP, four sand-coated CFRP-RC
slabs were simulated with reinforcement ratio of 0.35, 0.40, 0.45 and 0.7%, to obtain the
minimum ratio to satisfy code requirements.
Figure 6.16 (a and b) shows typical cracking pattern for FEM at the notched mid-span location.
Using a reinforcement ratio of 0.70% sand-coated CFRP bars resulted in a final crack width and
average bar strain of 0.21 mm and 660 με, respectively (Fig. 6.16 (c and d)). These values were
0.33 mm and 1400 με, respectively, for the counterpart slab with GFRP bars. This was s
expected due to lower modulus of elasticity GFRP bars compared to that of CFRP. Nevertheless,
the results for crack width and average strain on the bars at crack location (Fig. 6.16 (c and d))
show that the change in bar surface texture (sand-coated to ribbed-deformed bar) has
insignificant effect on the results. This may be attributed to the similar bond stress-slippage
behavior for sand-coated and ribbed bars (GFRP and CFRP) at low induced stress surrounding
the reinforcement in the vicinity of the crack (Malvar et al. 2003 and Alves et al. 2011). The
stress surrounding the reinforcement at crack location calculated by Gilbert’s model (Gilbert
1992) for sand-coated and ribbed-deformed CFRP bars were 0.73 and 0.74 MPa, respectively.
However, this value for sand-coated and ribbed-deformed GFRP bars was 0.62 and 0.63 MPa,
respectively.
Chapter 6: Numerical Analysis
133
Test results indicate that primarily width of the crack in the models reinforced with CFRP bars
varied depending on the reinforcement ratio crossing the crack. Figure 6.17 shows that
increasing the reinforcement ratio from 0.35 to 0.7%, decreased crack width and reinforcement
strain at crack location from 0.66 to 0.21 mm and from 2350 to 660 μɛ, respectively. Also, test
results indicate that a ratio of 0.45% can control the early-age crack width and reinforcement
strain in CFRP-RC bridge deck slabs subjected to shrinkage. In the model reinforced with 0.45%
CFRP bars, the maximum crack width and CFRP strain were 0.42 mm and 1890 μɛ, respectively.
These values are below the allowable code limit of 0.5 mm and 7650 μɛ (65% of CFRP ultimate
strain), respectively (CHBDC 2006).
Chapter 6: Numerical Analysis
134
15Table 6.4: Test matrix for the FEM
Name Concrete cover
(B.&T.)(mm)
Concrete
strength
(28days)
(MPa)
Reinforcement
ratio (%)
Bar
spacing
(mm)
Bar type Stage
SG2
35&25 38
0.5
255
GFR/Sand
coated
Verification
SG3 0.7 GFR/Sand
coated
SG4 1.1 GFR/Sand
coated
SS 0.7 Steel/Ribbed
G.CS.30
35&25
30
0.7 255 GFR/Sand
coated
Parametric
study
Concrete
strength
G.CS.40 40
G.CS.50 50
G.CS.60 60
G.CS.70 70
G.CS.80 80
G.CC.5 5&5
38 0.7 255 GFR/Sand
coated
Parametric
study:
Concrete
cover
G.CC.15 15&15
G.CC.25 25&25
G.CC.35 35&35
G.CC.45 45&45
G.CC.55 55&55
G.CC.56 65&65
G.CC.75 75&75
G.CC.85 85&85
G.BS.96
35&25 38 0.7
96
GFR/Sand
coated
Parametric
study: Bar
spacing
G.BS.128 128
G.BS.153 153
G.BS.191 191
C.SC.0.70
35&25 38
0.70
255
CFR/Sand
coated Parametric
study: bond
type
C.RB.0.70 0.70 CFR/Ribbed
bar
C.SC.0.70 0.70 GFR/Ribbed
bar
G.RB.0.35
35&25 38
0.35
255
CFR/Sand
coated
Parametric
study: CFRP
bar G.RB.0.40 0.40
CFR/Sand
coated
G.RB.0.45 0.45 CFR/Sand
coated
* Total longitodinal reinforcement ratio, equally, in two layers (top and bottom)
16
Chapter 6: Numerical Analysis
135
Table 6.5: The predicted shrinkage value for different concrete strength according to the CEB-
MC-90/99 model
Concrete strength
(MPa)
Autogenous Shrinkage
(μɛ)
Drying Shrinkage
(μɛ)
Total Shrinkage
(μɛ)
30 58 112 170
40 81 100 181
50 104 88 192
60 127 79 206
70 148 70 218
80 168 62 230
83Fig. 6.13: Results of FEM for slabs with different concrete strength, (a) typical concrete stresses
in the Y direction (MPa) and cracking pattern (f’c = 30 MPa), and (b) development of crack width
and average reinforcement strain at cracking with time.
Chapter 6: Numerical Analysis
136
84Fig. 6.14: Results of FEM for slabs with different bar spacing: (a) typical concrete stresses in the
Y direction (MPa) and cracking pattern (for spacing: 255 mm), and (b) development of crack
width and average reinforcement strain at cracking with time.
85Fig. 6.15: Results of FEM for slabs with different concrete cover: (a) typical concrete stresses in
the Y direction (MPa) and cracking pattern (for cover: 5 mm), and (b) development of crack
width and average reinforcement strain at cracking with time.
Chapter 6: Numerical Analysis
137
86Fig. 6.16: Results of FEM for slabs with different bar type: (a) typical concrete stresses in the Y
direction (MPa) and cracking pattern for GFRP, (b) typical concrete stresses in the Y direction
(MPa) and cracking pattern for CFRP (c) development of crack width with time, and (d)
development of the bar strains at crack location for the FEM.
87Fig. 6.17: The crack width and average reinforcement strain (Top and Bot.) at cracking location
for the FE models reinforced with CFRP bars at 112 days.
Chapter7: Summary, Conclusions and Future Work
138
CHAPTER7: SUMMARY, CONCLUSIONS AND FUTURE WORK
7.1 SUMMARY
The current thesis investigated the effect of early-age cracking in bridge deck slabs reinforced
with GFRP bars subjected to different environmental conditions. The study consisted of two
phases: experimental and finite element analysis investigations. The experimental phase study
included eight full-size, cast-in-place deck slab prototypes, measuring 2500 mm long × 765 mm
wide × 180 mm thick, which were designed to investigate the influence of reinforcement ratio
and bar type (GFRP and steel) on transverse early-age cracking in bridge deck slabs under
different environmental conditions for a period of 112 days. The tested slabs were divided into
two series. Series (I), which included six specimens, was related to slabs investigating the effect
of changing the longitudinal reinforcement ratio and bar type subjected to shrinkage under
laboratory conditions. Series (II), which included two specimens, investigated the effect of
freezing-thawing and wetting-drying cycles on early-age cracking of GFRP-RC bridge deck
slabs. Series (I) consisted of five end-restrained RC slabs (SG1, SG2, SG3, SG4 and SS) and one
unrestrained/unreinforced; slab F. The five slabs included four GFRP-RC slabs, SG1, SG2, SG3
and SG4, with four different GFRP reinforcement ratios of 0.3, 0.5, 0.7 and 1.1%, respectively,
in addition to one steel-RC slab (SS) with a reinforcement ratio of 0.7%. Series (II) included two
slabs, G-FT and G-WD, reinforced with the minimum-acceptable reinforcement ratio of 0.7% as
obtained from Series (I). Series (II) was tested under freezing-thawing and wetting-drying
cycling conditions. All specimens (except slab F) were effectively anchored at their ends by
1473 × 1000 × 1200 mm concrete blocks, which were clamped (pre-stressed) to the laboratory
Chapter7: Summary, Conclusions and Future Work
139
strong floor. Also, the experimental results were compared to the predictions of a published
model (Gilbert 1992) that was originally developed for steel-RC members.
The analytical phase aimed at investigating the effect of different key variables including
concrete cover and concrete strength and bar type and spacing on the early-age behavior of FRP-
RC bridge deck slabs subjected to shrinkage using a finite element analysis. This phase included
constructing a finite element model (FEM) for the bridge deck slabs subjected to shrinkage using
ATENA software. The constructed FEM was verified against the experimental results and used
to conduct the parametric study.
7.2 CONCLUSIONS
7.2.1 Conclusions from the Experimental Testing of Series (I) Specimens
Based on the experimental variables and laboratory conditions implemented for specimens in
Series (I), the following conclusions can be drawn:
1. The longitudinal minimum reinforcement ratio of 0.7%, recommended by CHBDC, can
conservatively control the early-age crack width and reinforcement strain for GFRP-RC
bridge deck slabs under normal laboratory conditions.
In Slab S3 (with 0.7%), the maximum measured crack width and GFRP strain were
0.33 mm and 1520 μɛ, respectively. These values are well below the allowable code
limit of 0.5 mm and 5250 μɛ (25% of GFRP ultimate strain), respectively (CHBDC
2006).
As the GFRP reinforcement ratio increased, the average crack width at mid-span and
strain in GFRP bars decreased. Also, the average strain readings of the instrumented
bars (top and bottom) in the vicinity of the crack decreased from 3750 to 1005 μɛ as
Chapter7: Summary, Conclusions and Future Work
140
the reinforcement ratio increased from 0.3 to 1.1%. These were expected due to the
increased concrete section stiffness with the higher reinforcement ratio.
The concrete internal strain at cracking decreased from 336 to 233 μɛ as the
reinforcement ratio increased from 0.3 to 1.1% due to increasing the level of internal
restraint.
2. The modulus of elasticity of reinforcement has a significant effect on early-age crack width
in RC bridge deck slabs subjected to restrained shrinkage.
In specimens SG3 and SS reinforced with GFRP and steel reinforcement ratio of
0.7% under laboratory conditions, the early-age crack width and reinforcement strain
at vicinity of the first crack reached to 0.33 and 0.18 mm, and 1520 and 440 με,
respectively, after 112 days. Due to lower modulus of elasticity of GFRP bars, the
crack width and average reinforcement strain in GFRP-RC bridge deck slabs were
two and three times, respectively, larger than the slab reinforced with steel bars.
7.2.2 Conclusions from the Experimental Testing of Series (II) Specimens
Based on the test procedures and environmental conditions adopted in Series (II), the following
conclusions can be drawn:
1. The minimum longitudinal reinforcement ratio of 0.7%, recommended by CHBDC, for
GFRP-RC bridge deck slabs satisfied the serviceability requirements of CHBDC after being
subjected to the simulated exposures of freezing-thawing and wetting-drying cycles.
The maximum measured crack width and GFRP strains did not exceed 0.46 mm and
2250 μɛ, respectively. These values are, respectively, less than the allowable code
limits of 0.5 mm and 5250 μɛ, which represents 25% of GFRP ultimate strain
(CHBDC 2006).
Chapter7: Summary, Conclusions and Future Work
141
Under freezing-thawing conditions, the crack width reached its maximum and
minimum values at +4 °C (thawing) and -18 °C (freezing), respectively, in each
cycle. This behavior is attributed to the volumetric expansion of the critically
saturated slab during freezing, which led to partial closure of the crack opening. Upon
relieving the expansion pressure during thawing periods, the crack width increased up
to 0.42 mm (in the last cycle), which is 40 and 27% higher than the crack width
measured before the freezing-thawing exposure and in the specimen subjected to
laboratory exposure (slab SG3), respectively.
In the specimen under wetting-drying conditions, the lower crack width and
reinforcement strain recorded during the wetting periods can be attributed to swelling
of the slab due to the increase in relative humidity, which led to partial closure of the
crack opening. Subsequently, excessive drying shrinkage of the slab increased the
crack width and reinforcement strain in the drying period.
The Ultrasonic Pulse Velocity (UPV) test results show a general reduction of
Dynamic Modulus of Elasticity (DME) for the concrete exposed to cyclic conditions,
which indicates the existence of fissures and micro-cracks in the cementitious matrix.
The Rapid Chloride Penetrability Test (RCPT) and microstructural analysis indicated
that the specimens extracted from the slab subjected to wetting-drying cycles yielded
relatively higher penetration depths and more internal micro-cracks in the vicinity of
the crack location, which signifies that the pore structure was highly interconnected in
these specimens. This can be attributed to a higher intensity of micro-cracks due to
the matrix fatigue resulting from high strain fluctuations of repetitive swelling and
drying shrinkage in the wetting-drying exposure. These results are consistent with the
Chapter7: Summary, Conclusions and Future Work
142
higher concrete and reinforcement strain values for specimen G-WD exposed to
drying conditions.
7.2.3 Conclusions from Numerical Modeling (ATENA and Gilbert’s Model)
1. Gilbert’s model (Gilbert 1992), to predict width of shrinkage cracks and stresses in
reinforcement, can be applied to GFRP-RC deck slabs by modifying the coefficient so to 0.8
instead of 1.33, which was originally proposed for steel-RC members.
Under laboratory conditions, the measured width of shrinkage cracks and stresses in
GFRP agreed with most results from the modified Gilbert’s model (Gilbert 1992)
within 16% error. The results indicate that more refinement to Gilbert’s model is still
needed to be fully applicable to FRP-RC slabs (especially for structures reinforced
with small bar diameter), which is recommended for future research.
2. Neither the reinforcement surface texture nor the concrete cover had a significant effect on
the early-age cracking behavior of FRP-RC bridge deck slabs subjected to shrinkage.
However, reducing bar spacing and concrete strength resulted in a decrease in crack width.
The constructed FEM was able to analyze FRP-RC bridge deck slabs subjected to
restrained shrinkage. The FEM could predict the maximum crack width and the main
cracking pattern as well as the strains developed in the reinforcement at the vicinity of
the crack to a reasonable degree of accuracy (within 6 to 10% for crack width and
reinforcement strain at the crack location, respectively).
The results of finite element analysis and experimental study were not consistent in
terms of freezing-thawing and wetting-drying cycles, which can be attributed to the
effect of internal water expansion and evaporation mechanism due to sub-zero and
Chapter7: Summary, Conclusions and Future Work
143
elevated (35 °C) temperatures, respectively, which are not considered in the FE
concrete material model.
The results indicate that, in RC bridge deck slabs, increasing concrete strength
aggravates early-age cracking. This serviceability issue is attributed to the increased
aoutogenous shrinkage and higher induced tensile stresses in the slabs with a higher
concrete strength. At 112 days, as concrete strength increased from 30 to 80 MPa, the
crack width and reinforcement strain at crack location grew from 0.33 to 0.48 mm
and from 1400 to 2020 με, respectively.
In RC bridge deck slabs subjected to restrained shrinkage, reducing the bar spacing
results in simultaneous decrease in crack width and increase in reinforcement strain at
crack location. In the FEM with constant reinforcement ratio of 0.7%, decreasing bar
spacing from 255 to 96 mm increased the average value of reinforcement strain from
1400 to 1880 με and reduced crack width from 0.34 to 0.29 mm.
Test results indicate that for the FRP-RC members subjected to axial tension
(shrinkage), the crack-width and strain in the bars at crack location are less dependent
on the thickness of concrete cover. This is due to the fact that shrinkage cracks are
full-depth and parallel-sided.
Due to the relatively lower modulus of elasticity of GFRP bars, the crack width and
average reinforcement strain in GFRP-RC slab were 1.6 and 1.1 times, respectively
larger than those of the corresponding slab reinforced with similar CFRP
reinforcement ratio of 0.7%. Nevertheless, the results for crack width and average
strain in the bars at crack location show that the change in bar surface texture (sand-
coated to ribbed-deformed bar) has insignificant effect on the results.
Chapter7: Summary, Conclusions and Future Work
144
3. The reinforcement ratio of 0.45% CFRP can keep the early age crack width within the
allowable limits of the CHBDC (2006).
FEM results indicate that a CFRP reinforcement ratio of 0.45% can keep the early-
age crack width and reinforcement strain within allowable code limits (CHBDC
2006) of 0.5 mm and 7650 με (65% of CFRP ultimate strain), respectively. This is
attributed to the high stiffness of slab section in the CFRP-RC bridge deck slabs.
7.3 Engineering Significance
The reinforcement ratio of 0.7% GFRP can be used as minimum reinforcement for GFRP-RC
bridge deck slabs cast with normal strength concrete incorporating 13% silica fume by mass of
binder (to stimulate a critical case for early-age shrinkage of concrete). This reinforcement ratio
satisfied the serviceability requirements of the CHBDC (CSA 2006) after being subjected to
severe environmental conditions. Also, a CFRP reinforcement ratio of 0.45% can keep the early-
age crack width and reinforcement strain within allowable code limits (CSA 2006) under normal
conditions.
7.4 RECOMMENDATIONS FOR FUTURE WORK
The research findings are extremely useful to the knowledge in this field and can be helpful in
the development of Canadian and international codes addressing this subject. Based on the
findings and conclusions of the current work, the following recommendations are made for
future research:
1. As the present study was carried out using mainly GFRP reinforcement, more experiments
should be conducted on slabs reinforced with other FRP reinforcement such as carbon or
aramid FRP bars.
Chapter7: Summary, Conclusions and Future Work
145
2. Further experimental and analytical studies are needed to investigate the behavior of FRP-
RC slabs with a wider range of reinforcement ratios, volume-to-surface ratios and slab
thicknesses.
3. Since the internal relative humidity plays an important role on early-age behavior of the
concrete slabs subjected to freezing-thawing environments, further experimental studies
are needed to investigate the early-age cracking in bridge deck slabs subjected to these
conditions with different internal relative humidity ranges.
4. Research is further needed to investigate the effect of early-age cracking when longitudinal
and transverse FRP reinforcement is used.
5. Admixtures have an effect on the cracking tendencies of concrete structures. The primary
admixtures that affect this cracking tendency are water reducers, retarders, accelerators and
highly reactive mineral admixtures. More research is needed to study the effect of these
admixtures on early-age cracking of bridge deck slabs reinforced with FRP bars.
6. Finite elements results are contradictory to those obtained from the specimens subjected to
freezing-thawing and wetting-drying conditions in the experimental study. Therefore,
further research is required to provide enough data that could contribute to build a robust
FEM under freezing-thawing and wetting-drying environments.
References
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Appendix A
A-1
APPENDIX A
SHRINKAGE PREDICTION MODELS
Appendix A
A-2
A-1: DIFFERENT SHRINKAGE PREDICTION MODELS
ACI 209.2R-08 recommended to use the following method to predict time dependent shrinkage
in the concrete; ACI 209R-92 (ACI Committee 209 1992), Bažant-Baweja B3 (Bažant and
Baweja 1995, 2000), CEB MC90-99 (Muller and Hillsdorf 1990; CEB 1991, 1993, 1999), and
GL2000 (Gardner and Lockman 2001). According the parameter ranges for each model (Table
App.1), ACI 209.2R-8, Bažant-Baweja B3, and GL200 can be used for the curing time of 1 day.
The other methods predict the shrinkage of the concrete with curing time at least 14 days.
Nevertheless CEB MC90-99 has been adjusted to take into account the particular characteristics
of concrete strength (for high concrete strength).
17Table A-1: Parameter ranges of each model
Input variables ACI 209R-92 Bažant-Baweja B3 GL2000 CEB MC90-99
fcm28 (MPa) — 17 to 70 16 to 82 15 to 120
a/c — 2.5 to 13.5 — —
Cement content (kg/m3) 279 to 446 160 to 720 — —
w/c — 0.35 to 0.85 — —
Relative humidity (%) 40 to 100 41 to 100
20 to
100 40 to 100
Type of cement I,II I,II,III I,II,III I,II,III
Moist cured ≥ 1 days ≥ 1 days
≥ 1
days ≥ 14 days
Steam cured 1 to 3 days — — —
Loading time ≥ 7 days ≥ 1 days
≥ 1
days ≥ 1 days
a/c: air to cement ratio, w/c: water to cement ratio, fcm28: concrete compressive strength in 28 days.
Appendix A
A-3
In this research the following input values were used to predict the amount of shrinkage (Table
A-2):
18Table A-2: Input values for theoretical equations to predict shrinkage
Thickness mm 180
Specified 28-day strength f'c f'c (MPa) 38
Ambient relative humidity h (%) 70
Temprature T (0C) 20
Valume /surface V/S (mm) 180
Shape - Infinite Slab
Curing time Tc (days) 1
Curing conditions - air
Age at loading T0 (days) 1
Applied stress range ks (%) 40
Cement type GU I
Max agg. Size mm 20
Cement content c (kg/m3) 420
Water content w (kg) 170
water-cement ratio w/c 0.40
Aggregate-cement ratio a/c 4
Fine agg. Percentage ψ (%) 40
Air content α (%) 6
Slump s (mm) 140
Unit weight of concrete γc (kg/m3) 2450
A-1.1 ACI 209R-92 Model Solution:
Nominal ultimate shrinkage strain εshu = 780 × 10–6
Moist curing correction factor γsh,tc = 1.202 – 0.2337log(tc)
Ambient relative humidity factor γsh,RH = 1.40 – 1.02h
Appendix A
A-4
Volume-to-surface ratio factor γsh,vs = 1.2e[–0.00472(
V/S)]
Slump of fresh concrete factor γsh,s = 0.89 + 0.00161
Fine aggregate factor γsh,ψ = 0.30 + 0.014ψ if ψ ≤ 50%
Cement content factor γsh,c = 0.75 + 0.00061c
Air content factor γsh,α = 0.95 + 0.008α ≥ 1
Cumulative correction factor γsh = γsh,tc×γsh,RH×γsh,vs×γsh,s×γsh,ψ×γsh,c×γsh,α
Ultimate shrinkage strain εshu = 780γsh × 10–6
Shrinkage time function f(t,tc) = [(t – tc)α/(f + (t – tc)
α)]
A-1.2 Bažant-Baweja B3 Model Solution
Ambient relative humidity factor kh = 12.74 – 12.94h if 0.98 < h < 1
Cement type factor α1 = 1
Curing condition factor α2 = 1
Nominal ultimate shrinkage εsᴂ = –α1α2 [0.019w2.1
fcm28–0.28
+ 270] ×10–6
Member shape factor ks = 1
Shrinkage half-time τsh = 0.085tc–0.08fcm28–0.25 [2ks (V/S)] 2
Time dependence factor Ecm607/Ecm(tc+τsh) = 1.0805/[(tc + τsh)/(4 + 0.85(tc + τsh))]0.5
Ultimate shrinkage strain εsh∞ = –εs∞Ecm607/Ecm(tc+τsh)
Shrinkage time function S (t – tc) = tanh[(t – tc)/τsh]0.5
Shrinkage strains εsh(t,tc) = –εsh∞khtanh[(t – tc)/τsh]0.5
Appendix A
A-5
A-1.3 GL2000 model solution
Cement type factor k = 1
Ultimate shrinkage strain
Ambient relative humidity factor β(h) = (1 – 1.18h4)
Shrinkage time function β(t – tc) = [(t – tc)/{t – tc + 0.12(V/S)2}]
0.5
Shrinkage strains εsh(t,tc) = εshuβ(h)β(t – tc)
A-1.4 CEB MC90-99 model solution:
Autogenous shrinkage εcas(t)+ Drying shrinkage εcds(t,tc)
εsh(t,tc) εsh(t,tc) = εcas(t) + εcds(t,tc)
a) Autogenous shrinkage εcas(t)
Cement type factor αas = 700
Notional autogenous shrinkage εcaso(fcm28) = –αas[(fcm28/fcmo)/{6 + (fcm28/fcmo)}]2.5
× 10–6
Autogenous shrinkage time function βas(t) = 1 – exp[–0.2(t/ti)0.5
]
Autogenous shrinkage strains εcas(t) = εcaso(fcm28)βas(t)
b) Drying shrinkage εcds(t,tc)
Cement type factors αds1 = 4 αds2 = 0.12
Notional drying shrinkage coefficient εcdso(fcm28) = [(220 + 110αds1)exp(–αds2 fcm28/fcmo)] ×10–6
Ambient relative humidity factor βRH(h) = –1.55[1 – (h/ho)3] for 0.4 ≤ h < 0.99βs1 where βs1 =
[3.5fcmo/fcm28]0.1
≤ 1.0
Drying shrinkage time function βds(t – tc) = [{(t – tc)/1}/{350([(V/S)/(V/S)o]2 + (t – tc)/ti}]0.5
Drying shrinkage strains εcds(t,tc) = εcdso(fcm28)βRH(h)βds(t – tc)
Appendix A
A-6
Table App. 3 shows the calculated shrinkage value according to different model solutions. While
Table App. 4 represent calculated shrinkage value used in the analytical section for different
concrete strength of 20, 30, 40, 50, 60, 70 and 80 GPa.
19Table A-3: The calculated shrinkage value according to different model solutions
t (days) ACI 209R-92 Bažant-Baweja B3 GL2000 Average
1 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2 -1.76E-06 -1.84E-05 -2.11E-05 -1.38E-05
3 -3.52E-06 -2.61E-05 -2.98E-05 -1.98E-05
4 -5.26E-06 -3.19E-05 -3.65E-05 -2.45E-05
5 -7.00E-06 -3.68E-05 -4.21E-05 -2.86E-05
6 -8.72E-06 -4.11E-05 -4.70E-05 -3.23E-05
7 -1.04E-05 -4.50E-05 -5.15E-05 -3.56E-05
8 -1.21E-05 -4.86E-05 -5.55E-05 -3.88E-05
9 -1.38E-05 -5.19E-05 -5.93E-05 -4.17E-05
10 -1.55E-05 -5.51E-05 -6.29E-05 -4.45E-05
11 -1.72E-05 -5.80E-05 -6.62E-05 -4.71E-05
12 -1.89E-05 -6.08E-05 -6.94E-05 -4.97E-05
13 -2.05E-05 -6.35E-05 -7.24E-05 -5.21E-05
14 -2.22E-05 -6.60E-05 -7.53E-05 -5.45E-05
15 -2.38E-05 -6.85E-05 -7.81E-05 -5.68E-05
16 -2.54E-05 -7.09E-05 -8.07E-05 -5.90E-05
17 -2.70E-05 -7.31E-05 -8.33E-05 -6.12E-05
18 -2.86E-05 -7.54E-05 -8.58E-05 -6.33E-05
19 -3.02E-05 -7.75E-05 -8.82E-05 -6.53E-05
20 -3.18E-05 -7.96E-05 -9.05E-05 -6.73E-05
21 -3.34E-05 -8.16E-05 -9.28E-05 -6.93E-05
22 -3.50E-05 -8.36E-05 -9.50E-05 -7.12E-05
23 -3.65E-05 -8.55E-05 -9.72E-05 -7.31E-05
24 -3.81E-05 -8.74E-05 -9.93E-05 -7.49E-05
25 -3.96E-05 -8.92E-05 -1.01E-04 -7.67E-05
26 -4.12E-05 -9.10E-05 -1.03E-04 -7.85E-05
27 -4.27E-05 -9.27E-05 -1.05E-04 -8.02E-05
28 -4.42E-05 -9.45E-05 -1.07E-04 -8.20E-05
90 -1.24E-04 -1.66E-04 -1.85E-04 -1.59E-04
91 -1.26E-04 -1.67E-04 -1.86E-04 -1.60E-04
92 -1.27E-04 -1.68E-04 -1.87E-04 -1.60E-04
93 -1.28E-04 -1.69E-04 -1.88E-04 -1.61E-04
94 -1.29E-04 -1.69E-04 -1.89E-04 -1.62E-04
108 -1.44E-04 -1.80E-04 -2.00E-04 -1.75E-04
109 -1.45E-04 -1.81E-04 -2.01E-04 -1.76E-04
110 -1.46E-04 -1.82E-04 -2.02E-04 -1.76E-04
111 -1.47E-04 -1.83E-04 -2.03E-04 -1.77E-04
112 -1.48E-04 -1.83E-04 -2.04E-04 -1.78E-04
Appendix A
A-7
20Table A-4: The calculated shrinkage value according to different concrete compressive strength
(CEB MC90-99 model solution)
f'(c) (MPa)
Time
(days) 30
40 50 60 70 80
0 0 0 0 0 0 0
1 -1.19E-05 -1.67E-05 -2.15E-05 -2.61E-05 -3.05E-05 -3.46E-05
2 -1.61E-05 -2.27E-05 -2.92E-05 -3.55E-05 -4.14E-05 -4.70E-05
3 -1.92E-05 -2.70E-05 -3.47E-05 -4.22E-05 -4.92E-05 -5.59E-05
4 -2.16E-05 -3.04E-05 -3.91E-05 -4.75E-05 -5.54E-05 -6.29E-05
5 -2.36E-05 -3.32E-05 -4.28E-05 -5.19E-05 -6.06E-05 -6.88E-05
6 -2.54E-05 -3.57E-05 -4.59E-05 -5.58E-05 -6.51E-05 -7.39E-05
7 -2.69E-05 -3.79E-05 -4.87E-05 -5.92E-05 -6.91E-05 -7.84E-05
8 -3.97E-05 -4.99E-05 -6.02E-05 -7.02E-05 -7.97E-05 -8.87E-05
9 -4.57E-05 -5.59E-05 -6.62E-05 -7.62E-05 -8.58E-05 -9.49E-05
10 -5.04E-05 -6.07E-05 -7.11E-05 -8.12E-05 -9.10E-05 -1.00E-04
11 -5.45E-05 -6.49E-05 -7.54E-05 -8.57E-05 -9.56E-05 -1.05E-04
12 -5.82E-05 -6.86E-05 -7.93E-05 -8.97E-05 -9.98E-05 -1.09E-04
13 -6.15E-05 -7.20E-05 -8.28E-05 -9.34E-05 -1.04E-04 -1.13E-04
14 -6.46E-05 -7.52E-05 -8.61E-05 -9.68E-05 -1.07E-04 -1.17E-04
15 -6.74E-05 -7.82E-05 -8.92E-05 -1.00E-04 -1.11E-04 -1.21E-04
16 -7.01E-05 -8.10E-05 -9.21E-05 -1.03E-04 -1.14E-04 -1.24E-04
17 -7.27E-05 -8.36E-05 -9.48E-05 -1.06E-04 -1.17E-04 -1.27E-04
18 -7.51E-05 -8.61E-05 -9.74E-05 -1.09E-04 -1.19E-04 -1.30E-04
19 -7.74E-05 -8.85E-05 -9.99E-05 -1.11E-04 -1.22E-04 -1.33E-04
20 -7.96E-05 -9.07E-05 -1.02E-04 -1.14E-04 -1.25E-04 -1.35E-04
21 -8.17E-05 -9.29E-05 -1.04E-04 -1.16E-04 -1.27E-04 -1.38E-04
22 -8.37E-05 -9.50E-05 -1.07E-04 -1.18E-04 -1.29E-04 -1.40E-04
23 -8.57E-05 -9.70E-05 -1.09E-04 -1.20E-04 -1.32E-04 -1.43E-04
24 -8.76E-05 -9.90E-05 -1.11E-04 -1.22E-04 -1.34E-04 -1.45E-04
25 -8.94E-05 -1.01E-04 -1.13E-04 -1.25E-04 -1.36E-04 -1.47E-04
26 -9.12E-05 -1.03E-04 -1.15E-04 -1.26E-04 -1.38E-04 -1.49E-04
27 -9.29E-05 -1.04E-04 -1.16E-04 -1.28E-04 -1.40E-04 -1.51E-04
28 -9.46E-05 -1.06E-04 -1.18E-04 -1.30E-04 -1.42E-04 -1.53E-04
29 -9.62E-05 -1.08E-04 -1.20E-04 -1.32E-04 -1.44E-04 -1.55E-04
30 -9.78E-05 -1.09E-04 -1.22E-04 -1.34E-04 -1.45E-04 -1.57E-04
31 -9.93E-05 -1.11E-04 -1.23E-04 -1.35E-04 -1.47E-04 -1.59E-04
32 -1.01E-04 -1.12E-04 -1.25E-04 -1.37E-04 -1.49E-04 -1.60E-04
33 -1.02E-04 -1.14E-04 -1.26E-04 -1.38E-04 -1.50E-04 -1.62E-04
34 -1.04E-04 -1.15E-04 -1.28E-04 -1.40E-04 -1.52E-04 -1.64E-04
35 -1.05E-04 -1.17E-04 -1.29E-04 -1.42E-04 -1.54E-04 -1.65E-04
36 -1.06E-04 -1.18E-04 -1.31E-04 -1.43E-04 -1.55E-04 -1.67E-04
Appendix A
A-8
37 -1.08E-04 -1.20E-04 -1.32E-04 -1.44E-04 -1.56E-04 -1.68E-04
38 -1.09E-04 -1.21E-04 -1.33E-04 -1.46E-04 -1.58E-04 -1.70E-04
39 -1.10E-04 -1.22E-04 -1.35E-04 -1.47E-04 -1.59E-04 -1.71E-04
40 -1.12E-04 -1.23E-04 -1.36E-04 -1.48E-04 -1.61E-04 -1.72E-04
41 -1.13E-04 -1.25E-04 -1.37E-04 -1.50E-04 -1.62E-04 -1.74E-04
42 -1.14E-04 -1.26E-04 -1.38E-04 -1.51E-04 -1.63E-04 -1.75E-04
43 -1.15E-04 -1.27E-04 -1.40E-04 -1.52E-04 -1.65E-04 -1.76E-04
44 -1.17E-04 -1.28E-04 -1.41E-04 -1.53E-04 -1.66E-04 -1.78E-04
45 -1.18E-04 -1.30E-04 -1.42E-04 -1.55E-04 -1.67E-04 -1.79E-04
46 -1.19E-04 -1.31E-04 -1.43E-04 -1.56E-04 -1.68E-04 -1.80E-04
47 -1.20E-04 -1.32E-04 -1.44E-04 -1.57E-04 -1.69E-04 -1.81E-04
48 -1.21E-04 -1.33E-04 -1.45E-04 -1.58E-04 -1.71E-04 -1.83E-04
49 -1.22E-04 -1.34E-04 -1.47E-04 -1.59E-04 -1.72E-04 -1.84E-04
50 -1.23E-04 -1.35E-04 -1.48E-04 -1.60E-04 -1.73E-04 -1.85E-04
51 -1.24E-04 -1.36E-04 -1.49E-04 -1.61E-04 -1.74E-04 -1.86E-04
52 -1.25E-04 -1.37E-04 -1.50E-04 -1.62E-04 -1.75E-04 -1.87E-04
53 -1.26E-04 -1.38E-04 -1.51E-04 -1.63E-04 -1.76E-04 -1.88E-04
54 -1.27E-04 -1.39E-04 -1.52E-04 -1.64E-04 -1.77E-04 -1.89E-04
55 -1.28E-04 -1.40E-04 -1.53E-04 -1.65E-04 -1.78E-04 -1.90E-04
56 -1.29E-04 -1.41E-04 -1.54E-04 -1.66E-04 -1.79E-04 -1.91E-04
57 -1.30E-04 -1.42E-04 -1.55E-04 -1.67E-04 -1.80E-04 -1.92E-04
58 -1.31E-04 -1.43E-04 -1.56E-04 -1.68E-04 -1.81E-04 -1.93E-04
59 -1.32E-04 -1.44E-04 -1.56E-04 -1.69E-04 -1.82E-04 -1.94E-04
60 -1.33E-04 -1.45E-04 -1.57E-04 -1.70E-04 -1.83E-04 -1.95E-04
61 -1.34E-04 -1.46E-04 -1.58E-04 -1.71E-04 -1.84E-04 -1.96E-04
62 -1.35E-04 -1.47E-04 -1.59E-04 -1.72E-04 -1.85E-04 -1.97E-04
63 -1.36E-04 -1.47E-04 -1.60E-04 -1.73E-04 -1.85E-04 -1.98E-04
64 -1.37E-04 -1.48E-04 -1.61E-04 -1.74E-04 -1.86E-04 -1.99E-04
65 -1.37E-04 -1.49E-04 -1.62E-04 -1.75E-04 -1.87E-04 -1.99E-04
66 -1.38E-04 -1.50E-04 -1.63E-04 -1.75E-04 -1.88E-04 -2.00E-04
67 -1.39E-04 -1.51E-04 -1.63E-04 -1.76E-04 -1.89E-04 -2.01E-04
68 -1.40E-04 -1.52E-04 -1.64E-04 -1.77E-04 -1.90E-04 -2.02E-04
69 -1.41E-04 -1.52E-04 -1.65E-04 -1.78E-04 -1.90E-04 -2.03E-04
70 -1.42E-04 -1.53E-04 -1.66E-04 -1.79E-04 -1.91E-04 -2.04E-04
71 -1.42E-04 -1.54E-04 -1.67E-04 -1.79E-04 -1.92E-04 -2.04E-04
72 -1.43E-04 -1.55E-04 -1.67E-04 -1.80E-04 -1.93E-04 -2.05E-04
73 -1.44E-04 -1.56E-04 -1.68E-04 -1.81E-04 -1.94E-04 -2.06E-04
74 -1.45E-04 -1.56E-04 -1.69E-04 -1.82E-04 -1.94E-04 -2.07E-04
75 -1.46E-04 -1.57E-04 -1.70E-04 -1.82E-04 -1.95E-04 -2.07E-04
76 -1.46E-04 -1.58E-04 -1.70E-04 -1.83E-04 -1.96E-04 -2.08E-04
Appendix A
A-9
77 -1.47E-04 -1.59E-04 -1.71E-04 -1.84E-04 -1.97E-04 -2.09E-04
78 -1.48E-04 -1.59E-04 -1.72E-04 -1.85E-04 -1.97E-04 -2.10E-04
79 -1.49E-04 -1.60E-04 -1.73E-04 -1.85E-04 -1.98E-04 -2.10E-04
80 -1.49E-04 -1.61E-04 -1.73E-04 -1.86E-04 -1.99E-04 -2.11E-04
81 -1.50E-04 -1.62E-04 -1.74E-04 -1.87E-04 -1.99E-04 -2.12E-04
82 -1.51E-04 -1.62E-04 -1.75E-04 -1.87E-04 -2.00E-04 -2.12E-04
83 -1.52E-04 -1.63E-04 -1.75E-04 -1.88E-04 -2.01E-04 -2.13E-04
84 -1.52E-04 -1.64E-04 -1.76E-04 -1.89E-04 -2.01E-04 -2.14E-04
85 -1.53E-04 -1.64E-04 -1.77E-04 -1.89E-04 -2.02E-04 -2.14E-04
86 -1.54E-04 -1.65E-04 -1.77E-04 -1.90E-04 -2.03E-04 -2.15E-04
87 -1.54E-04 -1.66E-04 -1.78E-04 -1.91E-04 -2.03E-04 -2.16E-04
88 -1.55E-04 -1.66E-04 -1.79E-04 -1.91E-04 -2.04E-04 -2.16E-04
89 -1.56E-04 -1.67E-04 -1.79E-04 -1.92E-04 -2.05E-04 -2.17E-04
90 -1.56E-04 -1.68E-04 -1.80E-04 -1.93E-04 -2.05E-04 -2.18E-04
91 -1.57E-04 -1.68E-04 -1.81E-04 -1.93E-04 -2.06E-04 -2.18E-04
92 -1.58E-04 -1.69E-04 -1.81E-04 -1.94E-04 -2.07E-04 -2.19E-04
93 -1.58E-04 -1.70E-04 -1.82E-04 -1.95E-04 -2.07E-04 -2.19E-04
94 -1.59E-04 -1.70E-04 -1.83E-04 -1.95E-04 -2.08E-04 -2.20E-04
95 -1.60E-04 -1.71E-04 -1.83E-04 -1.96E-04 -2.08E-04 -2.21E-04
96 -1.60E-04 -1.72E-04 -1.84E-04 -1.96E-04 -2.09E-04 -2.21E-04
97 -1.61E-04 -1.72E-04 -1.84E-04 -1.97E-04 -2.09E-04 -2.22E-04
98 -1.62E-04 -1.73E-04 -1.85E-04 -1.98E-04 -2.10E-04 -2.22E-04
99 -1.62E-04 -1.73E-04 -1.86E-04 -1.98E-04 -2.11E-04 -2.23E-04
100 -1.63E-04 -1.74E-04 -1.86E-04 -1.99E-04 -2.11E-04 -2.23E-04
101 -1.64E-04 -1.75E-04 -1.87E-04 -1.99E-04 -2.12E-04 -2.24E-04
102 -1.64E-04 -1.75E-04 -1.87E-04 -2.00E-04 -2.12E-04 -2.24E-04
103 -1.65E-04 -1.76E-04 -1.88E-04 -2.00E-04 -2.13E-04 -2.25E-04
104 -1.65E-04 -1.76E-04 -1.88E-04 -2.01E-04 -2.13E-04 -2.26E-04
105 -1.66E-04 -1.77E-04 -1.89E-04 -2.01E-04 -2.14E-04 -2.26E-04
106 -1.67E-04 -1.78E-04 -1.90E-04 -2.02E-04 -2.14E-04 -2.27E-04
107 -1.67E-04 -1.78E-04 -1.90E-04 -2.03E-04 -2.15E-04 -2.27E-04
108 -1.68E-04 -1.79E-04 -1.91E-04 -2.03E-04 -2.15E-04 -2.28E-04
109 -1.68E-04 -1.79E-04 -1.91E-04 -2.04E-04 -2.16E-04 -2.28E-04
110 -1.69E-04 -1.80E-04 -1.92E-04 -2.04E-04 -2.16E-04 -2.29E-04
111 -1.70E-04 -1.80E-04 -1.92E-04 -2.05E-04 -2.17E-04 -2.29E-04
112 -1.70E-04 -1.81E-04 -1.93E-04 -2.05E-04 -2.18E-04 -2.30E-04
Appendix A
A-10
According the CEB MC90-99 model solution the amount of total shrinkage is increasing with
increasing concrete strength, while drying shrinkage is decreasing with decreasing water content
in high strength concrete (Fig. App1).
88Fig. A-1: The final calculated shrinkage for different concrete strength (CEB MC90-99 model
solution).
0
50
100
150
200
250
20 30 40 50 60 70 80 90
Str
ain
(μ
ɛ)
Concrete strength (GPa)
Autoganeous shrinkage Drying shrinkage Total Shrinkage
Appendix B
B-1
APPENDIX B
CALCULATION OF FINAL CRACK WIDTH AND REINFORCEMENT STRAIN
Appendix B
B-2
B-1 GILBERTS PREDICTION MODEL
In this part, the crack width and bar strain for GFRP-RC bridge deck slabs subjected to shrinkage are predicted based on analytical
model developed for steel-RC members (Gilbert 1992).
Determination of final crack width and bar stress at cracking location using Gilbert’s model (Gilbert 1992) for all slabs:
21Table B-1: Input data for parameters used in Gilbert’s model
Slab L
(mm)
t
(mm)
AGFRP
(mm2)
db
(mm) ϕ* ε*
sh ft (7)
(MPa)
ft (28)
(MPa)
fc (3)
(MPa)
fc (28)
(MPa)
E c (3)
(MPa)
E c (28)
(MPa)
EGFRP
(MPa)
ft (GFRP)
(MPa)
SG1 2500 180 284 9.5 0.6 -3.48e-4 3.4 3.7 25 38 20200 21800 74351 1572
SG2 2500 180 508 12.7 0.6 -3.48e-4 3.4 3.7 25 38 20200 21800 69607 1759
SG3 2500 180 764 15.9 0.6 -3.48e-4 3.4 3.7 25 38 20200 21800 68297 1725
SG4 2500 180 1140 19.1 0.6 -3.48e-4 3.4 3.7 25 38 20200 21800 65374 1484
S 2500 180 508 16 0.6 -3.48e-4 3.4 3.7 25 38 20200 21800 200000 fy:546
G-WD 2500 180 764 15.9 0.6 -4e-4(dry)
2.86(wet) 3.4 3.7 25 41 20200 22200 68297 1725
G-FT 2500 180 1140 15.9 0.6
-2.84e-
4(thaw)
-2.6e-
4(freeze)
3.4 3.7 25 35 20200 21000 68297 1725
Appendix B
B-3
For specimen SG1:
The concrete area and reinforcement ratio are:
𝐴𝑐 = 𝐴𝑔𝑟𝑜𝑠𝑠 − 𝐴𝑆 = 765 × 180 − 792 = 136908 mm2
𝜌 =𝐴𝑠𝐴𝑐⁄ = 0.00578
The modular ratio is
𝑛 =𝐸𝑠𝐸𝑐(3)⁄ = 69607 20200⁄ = 3.44
The distance S0, over which the concrete and reinforcement stress vary is given by:
𝑆0 =𝑑𝑏10𝜌⁄ = 275 mm
The final effective modulus is
𝐸𝑒∗ =
𝐸𝑐(3)
1 + 𝜑∗⁄ = 20200 1 + 0.6⁄ = 12625 MPa
And the corresponding effective modular ratio is
𝑛∗ =𝐸𝑠𝐸𝑒∗⁄ = 69607 12625⁄ = 5.51
The ratio C1 is given by
𝑐1 =2𝑆0
3𝐿−2𝑆0=
2×275
3×2500−2×275= 0.0790
And the restraining force immediately after first cracking is obtained by
Ncr =nρftAc
C1+nρ(1+C1)=
3.44×0.00578×3.24×136908
0.079+3.44×0.00578×(1+0.079)=87895.30483 N
Appendix B
B-4
The concrete stress away from the crack immediately after first cracking is given by:
σc1 =(1+C1)Ncr
Ac=87895.3(1+0.079)
136908=0.6928
And the estimate of the average concrete stress in the period after first cracking is given by:
σav =σc1 + ft2
=0.6928 + 3.24
2= 1.96639
For long-term calculations, the final value for S0 over which the concrete and bars stress vary, is given by:
S0 =1.33db
10ρ= 365.55 mm
The final restraining force is
𝑁(∞) =−3𝐴𝑠𝑛
∗𝐸𝑠∆𝑢
2𝑠0𝑚−(3𝐿 − 2𝑠0𝑚)𝑛
∗𝐴𝑠2𝑠0𝑚
(𝜎𝑎𝑣 + 𝜀∗𝑠ℎ𝐸
∗𝑒) = 48176.3 N
The final bar stress at cracking obtained by
𝜎∗𝑠2 =𝑁(∞)
𝐴𝑠= 60.83 MPa
The final bar stress away from crack in obtained by
𝜎∗𝑠1 =−2𝑆0𝑚
3𝑙 − 2𝑆0𝑚𝜎∗𝑠2 +
3∆𝑢𝐸𝑠3𝑙 − 2𝑆0𝑚
= −13.4 MPa
The final concrete stress away from crack is obtained by
σ∗c1 =N(∞) − σ∗s1As
Ac= 0.43 MPa
The final crack width is now calculated by
𝑤 = −[𝜎∗𝑐1𝐸∗𝑒
(𝑠 −2
3𝑆0) + 𝜀
∗𝑠ℎ𝑆] = 0.39 mm
Appendix B
B-5
22 23Table B-2: The intermediate calculations for the theoretical predictions of crack width and the stress on the GFRP bars